"It's not day to day ... it could be a bit longer," Black said. "We're a little more concerned with this one. This could take a number of days or weeks."
Alonso is hitting .210 with five home runs and 22 RBIs in 229 at-bats. Tommy Medica got the start at first base Tuesday and Yasmani Grandal on Wednesday.
Alonso was limited to 334 at-bats last season after a right hand contusion in June sent him to the disabled list. He missed six weeks with the injury before returning in July. Alonso then essentially sat the entire month of September, not getting a single at-bat.
Black said this current injury isn't related to the hand injury from a year ago.
Goebbert was obtained last month from the A's for Kyle Blanks. Goebbert has played a handful of games at first base and can play the outfield. He's a left-handed hitter who is hitting .321 this month -- and .270 overall -- with El Paso.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.