Sharif Mozammel Haq is the second Awami League leader to be killed this week.
The BBC's Waliur Rahman in Dhaka says a group of armed men opened fire on Mr Haq as he came out of a restaurant in the city's crowded Gulistan area on Tuesday night.
He was taken to Dhaka Medical College Hospital where doctors pronounced him dead.
Upheaval
The Indian news agency PTI reported supporters of the Awami League rioted, damaging vehicles and shops and setting fire to a passenger bus in the Gulistan area in the city centre.
Police in Dhaka said they considered the shooting to be a criminal act caused by what they called business rivalries.
They have launched an investigation into the murder.
Awami League officials say Mr Haq had come to the area to attend a rally organised to protest against the killing of Manzurul Imam, a prominent Awami League leader killed in the south-western Khulna city on Monday.
The Awami League chief, Sheikh Hasina, blamed the government for the death of Mr Imam.
But local press reports said a banned Maoist group claimed it had carried out that attack.
The Awami League has called a countrywide strike on Thursday in protest at Mr Imam's murder.
Crisis
Around 10,000 members of Bangladesh's Awami League party gathered in Dhaka last December to try to decide how to revive the party's flagging fortunes.
It was defeated in general elections in 2001.
It now has less than a third of the seats in parliament.
Some of its most senior members are currently in prison accused of anti-state activities.