Manager A.J. Hinch says the injury is "hopefully not as bad as it could have been."
Signed as a minor league free agent, Benson is 1-1 with a 5.14 ERA in three starts. He went on the 15-day disabled list on Thursday after he was pulled from a start after two innings the previous day.
Right-handed reliever Leo Rosales, who went on the 15-day DL with a sprained right foot on Thursday, was to see a specialist on Friday.
And outfielder Conor Jackson, who's on the DL with a strained hamstring, will probably play three or four games in the minors before he returns, hopefully against the Astros next week.