The constable was placed in isolation and 11 more police personnel were quarantined at separate places, they said.
The Mandir Marg police station barracks, where the COVID-positive constable stayed, was sealed, the officials added.
Three more Delhi Police personnel, including a traffic inspector, tested positive for the infection on Thursday.
The 59-year-old traffic inspector was in charge of the Sangam Vihar area of Southern Traffic Range.
The other two are a 46-year-old head constable posted in Mahendra Park police station and an inspector deployed at the Lodhi Colony office of the Delhi Police Special Cell.
Contact-tracing is underway, the officials said. NIT IJTIJT