The Uruguay international, who leads the scoring charts for Atleti this season with 19 league goals, sustained the injury during a training session on Wednesday.
A statement released on Atletico's official website did not reveal the extent of the damage, but reports from Spain suggest the 34-year-old is facing three weeks out.
Suarez was already suspended for Sunday's trip to Real Betis and may also now miss league games with Eibar, Huesca and Athletic Bilbao before the end of April.
Former Barca striker Suarez has remained injury-free since joining Atleti at the start of the season, though he did spend time out after testing positive for coronavirus in November.
He has netted his 19 LaLiga goals in 26 appearances at a rate of one every 108.21 minutes, which is second only to Barcelona forward Lionel Messi (100.13) among those to have scored at least five times.
However, Atletico have won all four league games Suarez has not started this term and scored an average of 2.8 goals across those fixtures, compared to 1.6 with him in the line-up.
Diego Simeone will also be without suspended second top-scorer Marcos Llorente for next weekend's clash with Betis, possibly paving the way for Moussa Dembele to make his first start since joining on an initial loan deal from Lyon in January.