The 31-year-old veteran left Sunday's 3-2 loss to the Bruins midway through the third period and did not practice on Monday.
Lightning coach Jon Cooper did not say who would replace McDonagh in the lineup when the Eastern Conference second-round series resumes in Toronto. Luke Schenn and Braydon Coburn were both healthy scratches in Game 1.
McDonagh tallied one goal, 11 assists and 19 penalty minutes in 50 games during the 2019-20 regular season. He chipped in three assists during Tampa Bay's first-round series victory against the Columbus Blue Jackets.
McDonagh averaged 20:42 of ice time this season, second on the team to fellow blueliner Victor Hedman.
--Field Level Media