The two cases were discovered following swab tests carried out on Sunday, with the club immediately informing the health authorities upon learning the results.
Both players are asymptomatic and the rest of the squad tested negative, Milan confirmed in a statement released.
Calhanoglu and Hernandez are now isolating at home, leaving Milan without the duo for some key fixtures coming up in January.
The Serie A leader - which has lost just once in league action this season so far - visits Cagliari on Tuesday (AEDT), then hosts Atalanta at San Siro next Sunday.
There is also a Coppa Italia quarter-final clash with rival Inter looming on the horizon, that tie due to be played on 26 January.