Before the exchange of fire, demonstrators were filmed attacking a car
The violence erupted during a stand-off between supporters and opponents of Prime Minister Yingluck Shinawatra.
The shots were fired as demonstrators blockaded a building where ballot papers are being stored, in an attempt to prevent their distribution.
Protesters want the government replaced by an unelected "people's council".
The opposition has vowed to boycott Sunday's poll, which is likely to be won by Ms Yingluck.
Demonstrators accuse the prime minister of being under the control of her brother, ousted former leader Thaksin Shinawatra, who lives in self-imposed exile.
Troops deployed
Saturday's shooting incident took place in Bangkok's Laksi district, a stronghold of the prime minister's Pheu Thai party.
Sustained bursts of gunfire ricocheted off buildings after a tense stand-off between both sides, the BBC's Jonathan Head, in Bangkok, reports.
A number of people could be seen lying injured on the road, as exchanges of gunfire continued, forcing reporters and passers-by to flee for cover, our correspondent says.
It was not immediately clear whether those wounded were government supporters or opponents.
Before the attack, protesters had attacked a car and set off a series of small bombs.
The opposition movement - whose supporters are known as "yellow shirts" - has vowed to disrupt the election as much as possible, by preventing ballot papers from reaching polling stations.
Comment: What's the matter? Are they afraid they'll lose?
Meanwhile pro-government groups - or "red shirts" - have been ordered to monitor the poll, but not confront the protesters, for fear that violence would jeopardise the election.
The army earlier said it would increase the number of troops deployed in Bangkok for the polls on Sunday. Some 10,000 police will also patrol the streets.
Anti-government protesters want to replace hard won moves towards democracy in Thailand in 2009 with a return to explicit rule oligarchy.
The protests began in November, after the lower house backed a controversial amnesty bill that critics said would allow Ms Yingluck's brother to return.
Thaksin Shinawatra was ousted in a military coup in September 2006, accused of corruption and abuse of power.
He faces a two-year jail sentence if he returns to Thailand, after being convicted in absentia on a conflict-of-interest charge.
Ms Yingluck called early elections to quell the unrest, but demonstrators have vowed to block the poll from going ahead.
Correspondents say one election commissioner has predicted that 10% of polling stations will not be able to open at all on Sunday.
Because of disruption to candidate registration, the elections will also not deliver enough MPs for a quorum in parliament, meaning that by-elections will be needed before a government can be approved, extending the instability.
Last week, there were chaotic scenes as protesters tried to stop advance voters from casting their ballots.
Comment: As a general rule, when any 'protest' or 'revolutionary' movement has guns and bombs on its side, you can be pretty sure it's a move by the local oligarchs to subvert 'democracy' and reclaim power the only way it knows how.