Doctors raised the alarm after Ashya went missing from Southampton General Hospital
The five-year-old was removed from Southampton General Hospital by his parents, against medical advice, sparking an international hunt.
His parents were arrested in Spain, prompting a public outcry.
In her blog, hospital trust chief executive Fiona Dalton said paediatric oncology staff had been targeted.
She said: "When their email inboxes were full of personal abuse from strangers, and there were journalists camped on their front door, they were still worrying about how we could do the best thing for a small boy in Spain...
"Our switchboard and patient support services were overwhelmed with calls from irate members of the public... and many other people working here were being questioned by patients or the public about this situation, sometimes in a very aggressive way."
'Labelled kidnappers'
Parents Brett and Naghemeh King sparked a police hunt when they removed Ashya from hospital on 28 August after disagreeing with doctors about his treatment.
They wanted him to have proton beam therapy, which was not available to them on the NHS.
The couple were arrested in Spain and spent several days away from their son before the Crown Prosecution Service withdrew the European arrest warrant and they were released.
Ashya arrived at the Proton Therapy Centre in Prague on Monday by private jet from Spain.
After the family's arrival in Prague, Mr King said: "We've been labelled all sorts of things, from kidnappers to religious fanatics, we've had the police chasing us, we've been arrested, we've spent two days in a Spanish prison, we've had so many court cases.
"My son is everything to us so I've got no complaints. You know that, in comparison, what we've been through is nothing.
"We're just here, we've made it through, it's like we've been through a storm and we've come out the other end."
Comment: It's difficult to find any sympathy for these authoritarian staff members who violated the rights of a family who were only seeking to find the best treatment protocol for their son. It's becoming frightfully obvious that the State wishes to eliminate parental rights and we have now entered a new era of medical blackmail where many parents are finding the hard way how few rights they have, and how fascist their medical "care" system really is.
Ashya King case: Missing boy with brain tumor alive in Spain, parents arrested