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The two players, both regulars in Stefano Pioli's team, "tested positive in a molecular test" carried out on Saturday on the entire squad and were "immediately placed in quarantine at home", the club said.
AC Milan are already missing Croatian striker Ante Rebic and Bosnian midfielder Rade Krunic, who have not featured since their positive tests were announced on January 6.
It marks a new setback for Pioli who is also without Ismael Bennacer, Alexis Saelemaekers and Matteo Gabbia, who are all injured, while striker Rafael Leao is suspended.
His side have a three-point lead over city rivals Inter at the top of the table and will take the honorary title of "winter champion" on Monday if they win in Sardinia, the 18th round of the championship marking the halfway point in the title race.
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Hernandez and Calhanoglu are also likely to miss the Serie A match against Atalanta Bergamo next Saturday and the Italian Cup quarter-final against Inter on January 26.
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