Prado suffered the injury Friday night while running out a grounder against the Nationals.
Said Prado: "It has been a difficult year and a half for me."
Marlins manager Don Mattingly said there's no timetable yet for the return of the 34-year-old Prado, who will undergo further tests.
Hamstring and knee injuries limited Prado to 37 games last year, and he missed the first month of this season recovering from right knee surgery.
The Marlins recalled infielder J.T. Riddle from Triple-A New Orleans to fill Prado's roster spot. Riddle, who batted .250 in 70 games in 2017, had his rookie season derailed by left biceps tendinitis last July.
The Associated Press contributed to this report.