Manager Bud Black had revealed the intended move on Friday and the team made it official on Saturday.
Alonso bruised his right shoulder diving for a groundball in the eighth inning of the Padres' 11-0 loss to the Arizona Diamondbacks on Thursday night.
Almonte is with the major league club for the first time this season. He played in 32 games for San Diego last season, batting .239. He appeared in a combined 52 games with the Seattle Mariners in 2013 and 2014.