Ban was "deeply disturbed by the reported deaths" of the prisoners as they were being transferred to a different facility in Cairo, according to his spokesman Martin Nesirky.
"He calls for a full investigation to ascertain the facts surrounding this incident," Nesirky said yesterday.
Authorities said 37 Islamist detainees died after police fired tear gas in a bid to free an officer taken hostage by prisoners, as the inmates were being transferred to a north Cairo jail.
Ban also condemned a militant ambush of police buses in Egypt's Sinai Peninsula yesterday that left 25 policemen dead.
"The Secretary-General expresses the hope that the perpetrators will be swiftly identified and brought to justice," his spokesman said.