The injury occurred when Roberts stole second base Thursday against Tampa Bay. Following a headfirst slide, the 35-year-old had to be helped off the field.
Roberts was placed on the DL on Friday, hours before Baltimore's home opener against Minnesota. Roberts is expected to miss 2-to-4 weeks.
Infielder Yamaico Navarro, acquired in November from Pittsburgh, was recalled from Triple-A Norfolk.
Roberts played in only 115 games over the last three seasons because of injuries. He got through spring training without incident.