Taseer was shot 27 times and killed by Mumtaz Qadri, a member of his own security detail, at the posh Kohsar Market on January 4, 2011, in Islamabad for standing up for a Christian girl accused of blasphemy.
Qadri has become a divisive figure in Pakistan as he is hailed as a "hero" by some and denounced as murderer by others.
The mosque is in Ghori Town, a housing society near Khanna Bridge on way to the airport.
"The mosque was built to pay tribute to the man. The construction of the mosque, named after Mumtaz Hussain Qadri, began in October 2011. It is complete now and we have been offering prayers here since last one year," mosque's prayer leader Mohammad Ashfaq Sabri told PTI.
Also Read
"Please report the facts," Sabri said.
Reports say efforts are not to expand the mosque to cater to the large number of people who pray there.
The news of Mumtaz Qadri mosque comes just after it came to light that the Lal Masjid here has named its library after slain al-Qaeda chief Osama bin Laden.
Pakistan's Dawn newspaper first reported the matter yesterday.
Interestingly, civil society members and commoners observed candle vigils on Taseer's third death anniversary in January this year, rallies were also held in various parts of Pakistan by supporters of Qadri.
The late governor's daughter Sheherbano Taseer expressed her disgust at the development.
"This is disgusting. There's a Mumtaz Qadri mosque being built in VIP Ghouri Town in Faizabad," she tweeted.
Many twitter users in Pakistan have spoken out against naming the mosque after Qadri.