The Syrian Observatory for Human Rights said 42 prisoners and 15 militants died when the facility near Mayadin, in Deir al-Zour province, was hit on Monday.
The Deirezzor24 news website said dozens of civilians and Syrian rebel fighters were detained there.
A coalition spokesman said it was looking into the casualty reports.
Mayadin, which lies in the Euphrates river valley about 45km (28 miles) south-east of the city of Deir al-Zour, has been targeted frequently by coalition aircraft.