Taseer was one of the most moderate political voices in the main ruling Pakistan People's Party (PPP), which this week slumped into a major political crisis when its junior coalition partner walked out of the federal government.
He was outspoken against the Taliban and other Islamist militants based in the country's northwest. He most spoke out against controversial blasphemy laws.
Malik said the bodyguard had confessed that he killed the governor himself because he had called the blasphemy law a black law.
Police and anti-terror forces surround the area and the market closed after the attack.
Taseer made his money as a chartered accountant, setting up consultancy firms and a brokerage house, and with investments in telecommunications, the media, insurance and real estate before going into politics.
He served as minister for industry and production under former military ruler Pervez Musharraf from 2007 to 2008.