Flames could be seen on the ground as the man threw a petrol bomb with a firework attached of the car window
The attacker, a white man wearing a checked shirt, drove up to the centre in a white SEAT sports utility vehicle on Sunday morning.
He threw three petrol bombs with fireworks, one of which did not go off, a photographer said.
He reportedly drove to a nearby petrol station to kill himself, it was said. Police arrived minutes afterwards and cordoned off the area.
Witnesses at the scene described seeing the man laughing as he threw the bombs, as others reported hearing an explosion at the scene.
The extinguished fire from a petrol bomb at the migrant processing centre in Dover, following an attack on Sunday morning
He said: 'I was by my truck and I just heard this bang — I thought it was a bird scarer or something, so didn't really think much about it.
'Then a couple hours later I heard what happened, it was like all hell broke loose.'
Eye witness Mark Williamson, 59, an international lorry driver from Leeds, was on the scene moments after the driver died.
He said: 'I saw the dead guy just after it happened. I was going to meet my mate for a coffee and I saw the fella in the white vehicle sort of hanging out the window.
Comment: It appears that there's no details as to just how the man committed suicide.
'The next minute, armed response turned up. It was surreal.'
Kent Police confirmed that the suspect died, with the force finding them at the nearby petrol station. A spokesperson added that two people from inside the immigration premises have reported 'minor injuries'.
Gary Smith, 31, who saw the incident said that the man laughed as he threw the petrol bombs.
'I was walking over a nearby bridge and I could see him throwing the bombs,' he told The Sun.
'They we're making loud bangs. I think he threw about four or five. He was just laughing while he was doing it. It was crazy.'
'I heard what I thought was cannons going off and thought it must have been an event,' another witness told Kent Online.
'We paused the TV to hear. There were at least six or seven.
'To think it was actually explosions that we heard is just so upsetting. I really hope no one is hurt.'
The incident came after almost 1,000 migrants arrived in the UK after crossing the Channel on Saturday.
The area has been sealed off with police tape, while the vehicle, which is parked by the rear car wash, has been covered with blue tarpaulin.
A spokesperson for Kent Police told MailOnline: 'Officers established that two to three incendiary devices had been thrown outside and into the premises by a single suspect who arrived at the scene in a car.
'The suspect was identified, and very quickly located at a nearby petrol station, and confirmed deceased.'
The emergency services erect a tent around the car allegedly involved in an incident near the migrant processing centre
'The site remained open, however around 700 suspected migrants were relocated to Manston to ensure safety during the initial phase of the police investigation.
The Home Secretary tweeted: 'There was a distressing incident in Dover earlier today.
'I am receiving regular updates on the situation.
'My thoughts are with those affected, the tireless Home Office staff and police responding.
'We must now support those officers as they carry out their investigation.'
Immigration Minister Robert Jenrick will visit both Dover and Manston over concerns about tensions and overcrowding at the immigration centres, ITV reported.
A view of the docks and the migrant processing centre in Dover, Kent, following the incident
Mr Jenrick will visit both Dover and the Manston processing centre to 'take charge of the situation', Ms Elphicke said.
A Home Office spokeswoman said: 'We are aware of an incident at Western Jet Foil, Dover and police are in attendance. It would not be appropriate to comment further at this stage.'
Kent Police stated they were called at 11.22am to The Viaduct, where 'two to three incendiary devices' had caused a fire.
Kent Fire and Rescue Service confirmed its crews had put out fires. Nathalie Elphicke, the Conservative MP for Dover, said she was 'deeply shocked'.
Dozens of people were spotted being evacuated from the compound after the fire broke out
Nearly 40,000 have arrived in the UK so far this year after attempting the treacherous trip from France, crossing the world's busiest shipping lanes in dinghies and other small boats, provisional figures show.
Comment: It seems highly unlikely that these migrants could be arriving without the UK's border force having foreknowledge.
It is the highest number of arrivals in one day for a number of weeks, with more crossings taking place on Sunday morning.
The highest number in a single day was set on August 22 when 1,295 people arrived in the country.
It comes after an immigration watchdog said he was left 'speechless' by conditions at the Manston migrant processing centre in Kent, and warned the site has already passed the point of being unsafe.
Chief inspector of borders and immigration David Neal told MPs earlier this week that Manston was originally meant to hold between 1,000 and 1,600 people, but there were 2,800 at the site when he visited on Monday, with more arriving.
People arriving at a migrant processing centre shortly before the suspected arson attack in Dover
Migrants are meant to stay at the short-term holding facility, which opened in January, for 24 hours while they undergo checks before being moved into immigration detention centres or asylum accommodation - currently hotels.
The Sunday Times reported Home Secretary Suella Braverman has been accused of failing to act on legal advice received at least three weeks ago which warned migrants were being detained for unlawfully long periods.
A Home Office spokesperson said: 'The Home Secretary has taken urgent decisions to alleviate issues at Manston and source alternative accommodation. Claims advice was deliberately ignored are completely baseless.
'It is right we look at all available options so decisions can be made based on the latest operational and legal advice.
'The number of people arriving in the UK via small boats has reached record levels, which has put our asylum system under incredible pressure and costs the British taxpayer millions of pounds a day.'
Cabinet minister Michael Gove said the situation at Manston is 'deeply concerning', but he denied the Home Secretary ignored or dismissed legal advice.
'The situation in Manston is not what it should be,' he told Sky News's Sophy Ridge On Sunday programme.
'Everyone acknowledges that. We have more than 2,000 people there at the moment.'
The Liberal Democrats have called on the Government to publish the legal advice reportedly ignored by Ms Braverman.
Comment: Commentary and footage on the migrant crisis: