Hakimi is "totally asymptomatic" after his diagnosis emerged from the latest round of UEFA tests ahead of the Group B contest at San Siro.
The 21-year-old, in his first season at Inter after a superb spell with Borussia Dortmund, has played in all four of his team's Serie A matches this season, including their 2-1 loss in Saturday's Milan derby.
Hakimi will now enter a period of quarantine and can only come back once he has returned a negative result.
"Achraf Hakimi has tested positive in the latest round of UEFA checks (required by hygiene protocols) undertaken ahead of tonight's game against Borussia Monchengladbach," Inter said in a statement.
"The Inter full-back is totally asymptomatic and will now follow the procedure set out by the health protocol."
Inter have had to deal with a host of positive results in recent weeks.
Alessandro Bastoni and Radja Nainggolan have recovered while Ashley Young, Roberto Gagliardini, Ionut Radu and Milan Skriniar are among those still waiting for the all-clear to return.