Rosario will take a seat against southpaw Dallas Keuchel and the Astros on Tuesday.
Rosario went 2-for-4 with a double, a run scored, an RBI and a stolen base in Saturday's 11-4 loss to the Mariners.
Rosario is out of the lineup for Thursday's game against the Mariners, Mike Berardino of the St. Paul Pioneer Press reports.
Rosario has gone 3-for-16 with a stolen base through the Twins' first four games.
Rosario (triceps) started at DH and went 0-for-3 in Thursday's spring training game.
Rosario (triceps) was able to play catch Wednesday and expects slide into the Twins' lineup Thursday and Friday as the designated hitter, Rhett Bollinger of MLB.com reports.
Rosario (triceps) is scheduled to resume a throwing program Wednesday, Phil Miller of the Minneapolis Star Tribune reports.
Rosario is still dealing with tendinitis in his right triceps, Mike Berardino of the St. Paul Pioneer Press reports.
Rosario is out of the lineup against Cleveland on Thursday, MLBpressbox.com reports.
Rosario is not in the lineup Wednesday against the Rays, LaVelle E. Neal of the Star Tribune reports.