Mr Taseer, a senior member of the ruling Pakistan People's Party (PPP), was shot near a market popular with wealthy Pakistanis and foreigners.
He was taken to hospital where he died from his injuries.
Police say he was shot by a member of his own security detail as he got out of his car.
The BBC's Aleem Maqbool, in Islamabad, says Mr Taseer was one of Pakistan's most important political figures and his death will further add to political instability in the country.
The PPP-led government is dealing with a political crisis that erupted after a coalition partner quit.
It is unclear what motivated his assassin.
Mr Taseer had recently spoken out against the country's blasphemy law, prompting protests by Islamists.
Punjab is Pakistan's most populous province.