The security guard was arrested, Malik said. The shooting occurred at Islamabad's Kohsar Market, which is frequented by foreigners.
Taseer went into the market to make some purchases, and he was shot by his guard as he left, said Naeem Iqbal, spokesman for Islamabad police. He was taken to a hospital, where he died, apparently from blood loss.
Malik told Pakistan's GEO TV that Taseer was assassinated because he spoke out against Pakistan's blasphemy law.
A spotlight was put on the law in November when a Christian woman, Asia Bibi of Punjab province, was sentenced to death for blasphemy. A court found the 45-year-old woman guilty of defiling the name of the Prophet Mohammed during a 2009 argument with fellow Muslim field workers.
An investigation by a Pakistani government ministry found the charges against Bibi stemmed from "religious and personal enmity" and recommended her release.
In November, Taseer told CNN that Pakistan's President Asif Ali Zardari would pardon her.
"I mean, he's a liberal, modern-minded president and he's not going to see a poor woman like this targeted and executed," he said.
In addition, the government said it would review the law.
Reaction to the assassination from Pakistani officials was swift. Prime Minister Syed Yusuf Raza Gilani said in a statement he "strongly condemned" the incident. The Pakistan People's Party, the nation's ruling party, said it would observe two weeks of mourning over Taseer's death, according to GEO TV.
The English-educated Taseer created "a host of highly successful businesses," according to his official website, and is "the pioneer of cable television in Pakistan." He introduced the first English news channel in Pakistan, Business Plus.
His website describes Taseer as an activist who stood up to Pakistan's previous military leadership, calling it a "brutal and medievalistic dictatorship." He was arrested a total of 16 times, according to the website, placed on house arrest several times and spent time in "jails around the country."
He married twice and had six children, according to his website, which also contained a quote from him: "You live life once, you live it by your principles and you live it courageously -- that's what it's about." He lived in Lahore, Pakistan.
CNN's Chris Lawrence and Josh Levs contributed to this report.