The minister added none of the infected was in critical condition.
“All (inmates) are receiving treatment in hospital. There is no inmate in an intensive care unit; all are in a good state of health,” Gul told a televised news conference.
The minister would not disclose the locations of the prisons.
On April 13, Gul reported 17 coronavirus cases in Turkish prisons and said three of them had died of the disease.
There were no confirmed cases in closed prisons at the time, he said.
Turkey earlier this month started releasing around 90,000 inmates as part of a mass amnesty in a bit to reduce overcrowding and stop the spread of the epidemic in prisons.
The amnesty has been criticised for excluding opposition politicians, journalists, academics, civil servants and lawyers accused of terrorism-related charges.
The nationwide death toll from coronavirus, the respiratory disease caused by the novel coronavirus, climbed by 95 to 2,900, Health Minister Fahrettin Koca said on Monday.
The minister said that the number of positive cases rising to more than 112,000.