He's likely to miss four or more weeks, Padres general manager Josh Byrnes confirmed by email.
Alonso, who hasn't played since May 31, was hitting .284 with six home runs and 29 RBIs in 54 games. He suffered the injury when he was hit on the hand by a pitch against the Blue Jays on May 31.
"It was pretty painful," Alonso said Friday. "It's good news I was able to swing a bat in the first place. I'm shooting for three weeks, and I've already missed one week."
Alonso hit in the cage and took batting practice before Tuesday's game against the Dodgers but said his hand felt sore the following day, which was a result of the workload, according to manager Bud Black.
"It's a bummer for sure," said Black. "I thought we were going to avoid the DL with this one. I'm bummed for him. He likes playing. He's a durable guy."
In his absence, the Padres will use Kyle Blanks and Jesus Guzman at first base, though Mark Kotsay could see time there as well.
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.