Matsui has struggled with the health problem for much of spring training and was diagnosed with the condition earlier this week. The expected recovery time after the surgery is two weeks.
"We'll go down to the wire and see how he's progressing," Cooper said. "We want him on the roster and active so he can play."
Matsui was signed in December to take over at second base after Craig Biggio's retirement. He had 37s RBIs and four home runs with a .288 batting average last season for Colorado.
Also on Friday, Houston lefty Wandy Rodriguez strained a left oblique muscle and is listed as day-to-day. He threw just two pitches before leaving Houston's game against the Detroit Tigers on Friday night, which was called after one inning because of rain.