The attack, a dangerous new twist in the country's deadly political crisis, came as Zia stopped at the busy market while campaigning for a candidate running in mayoral polls due to take place in the capital later this month.
"She survived because it was a bullet-proof car," Zia's private secretary Shimul Biswas, who was with her during the attack, told AFP. "But the car still has bullet marks."
Local television footage showed scores of people attacking the convoy Zia was leading with metal rods, sticks and rocks. Media reports said the attackers were shouting pro-government slogans.
Police spokesman Alam blamed the violence on Zia's supporters, saying they had attacked protesters waving black flags at the opposition leader over violence in the last three months which has left at least 120 people dead.
But Biswas said at least six of Zia's security guards and supporters were injured in the attack, and that Zia later visited them in hospital.
The clashes were the latest episode in Bangladesh's deadly political crisis.
Zia, 69, had been confined to her office compound in Dhaka since January 3 after she threatened to lead a massive anti-government rally through the capital on the first anniversary of a disputed national election.
The stoppage was intended to force her bitter rival, Prime Minister Sheikh Hasina, to quit and pave the way for a new general election under a neutral administration.