Rojas was injured in the third inning Tuesday night, stumbling over first base while trying to avoid a double play. He remained on the ground for a while and needed help walking off the field.
The 30-year-old is in the midst of a productive season, hitting .289 in 108 games and playing a key role defensively for a young Miami team. Rojas will undergo tests Thursday to determine the severity of the injury.
"He's going to be missed,'' Marlins manager Don Mattingly said. "He's a guy that you depend on to kind of run things out there, always looking to make a play and always looking to win a game somehow.''
Infielder Deven Marrero was selected from Triple-A New Orleans to take Rojas' roster spot. He has played parts of four seasons with the Boston Red Sox and Arizona Diamondbacks, hitting .197 in 158 career games.
"We're getting a baseball player with experience and a guy that you know you can count on,'' Mattingly said. "You can put him on the field and he's going to know what to do with the baseball.''
Marrero signed with Miami in December but hasn't appeared in the majors this year.