City had been due to play Gladbach in Germany on February 24, but that plan has changed in the wake of new coronavirus protocols in Germany.
A statement from UEFA said: “UEFA can confirm that the UEFA Champions League Round of 16 first leg match between Borussia VfL 1900 Mönchengladbach and Manchester City FC will now take place at the Puskás Aréna in Budapest.
“The date of the match (24 February 2021) and kick-off time (21:00CET) will remain the same.
“UEFA would like to thank Borussia VfL 1900 Mönchengladbach and Manchester City FC for their close cooperation and support, as well as the Hungarian Football Federation for their assistance and agreeing to host the match in question.”
The second leg of City’s tie will take place at the Etihad Stadium, as planned, on March 16.