Alonso aggravated the shoulder, which was already sore from being hit with a pitch during the Padres' previous series at San Francisco. Padres manager Bud Black said team doctors told him Alonso seems likely to miss at least two weeks, though it could be longer.
Alonso is batting .333 in 26 games this season.
Black said the Padres will call up outfielder Abraham Almonte from Triple-A El Paso. Almonte is expected to join the Padres by Saturday.