The Omar al-Aswad mosque in the al-Faruq district of the old city centre was hit by a strike, three residents told the news agency.
Neighbouring houses were damaged or collapsed as a result of the blast.
The spokesman for the US-led coalition said he was not aware of a strike had targeted a mosque, according to Reuters.
The Iraqi military media officers said the war on IS was ongoing and troops were targeting the militants wherever possible, but did not say the mosque was targeted.
On Thursday Iraqi forces continued in their push on the west of Mosul as units cleared recently captured neighbourhoods.
"Iraqi units began in the early hours of Thursday to clear the neighbourhoods of Jawasaq, Tayaran and al-Mamoun," an officer in the Nineveh Operations Command told The New Arab.
"Meanwhile anti-terrorism forces continued in their push for the Mansour district, making significant progress," the officer said, adding that the troops were able to break IS defences in Wadi Hajar.
The operation to retake IS stronghold city of Mosul was launched on October 17.
IS overran large areas north and west of Baghdad in 2014, announcing a "caliphate" incorporating swathes of Iraq and Syria.
On Wednesday, a top US general said between 12,000 and 15,000 IS militants remain in Iraq and Syria, an indication of significant dwindling of the militant group’s forces.
Army Lieutenant General Stephen Townsend said among the many fighters killed in recent months are an "extraordinary number" of IS leaders, including many close to the group's elusive leader Abu Bakr al-Baghdadi.
"We have a specific campaign to hunt them and kill them," Townsend said in a video call from Baghdad.
"Almost all of Abu Bakr al-Baghdadi's inner circle has been killed in the last six months."
Still, he said about 2,000 IS fighters remain in and around western Mosul, defending the last portions of their former Iraqi bastion.
When the Mosul campaign began last year, officials estimated there to have been 3,000 to 5,000 IS fighters in and around the city.
Some of those fighters have fled west to the Tal Afar region and security forces have intercepted others who are trying to mingle with the civilian population "all over Iraq and Syria," Townsend said.
"We're focused on chasing them out in a sort of sequential campaign," he added.