The Premier League club were drawn against the Bundesliga team in Monday’s draw.
City topped Group C with 13 points, so were set to face a side that had finished second in their group. Monchengladbach qualified behind Real Madrid in Group B on eight points.
City reached the quarter-finals last season by defeating Real Madrid 4-2 on aggregate in the last 16, but Pep Guardiola’s team were beaten 3-1 by Lyon in the final eight – in a single-leg tie.
Champions League last-16 ties
Borussia Monchengladbach vs Manchester City
Atletico Madrid vs Chelsea
Sevilla vs Borussia Dortmund