The move is retroactive to May 26.
Hudson removed himself from Wednesday's game against the Cardinals after he reached first base on an infield single. An MRI late Wednesday showed a Grade 2 strain, which is considered a moderate strain.
"This wasn't going to be a quick-healing injury," Padres manager Bud Black said before Friday's game against the Nationals.
Hudson missed 13 games earlier this month with a strained right hamstring, an injury he suffered running the bases.
Hudson spent most of Friday afternoon getting treatment on his groin inside the visiting clubhouse at Nationals Park.
"It's baseball, it happens," Hudson said of the two injuries he's had this month. "It's just another small stepping stone. You've got to just take your time with injuries and do all that's needed to get better."
Hudson was hitting .245 when he suffered the hamstring strain in a game May 3 against the Pirates. He returned from the disabled list May 19, but was just 2-for-21 in his first seven games back, dropping his average to .217.
"Orlando is down, he wants to play," Black said. "When he's not playing, he's bummed. But he'll do everything he can on the disabled list to get himself healthy."
In Hudson's absence, the Padres will use Alberto Gonzalez and Eric Patterson at second base. Black did indicate that Logan Forsythe, who joined the team on Friday from Triple-A Tucson, will see time there as well.
Forsythe was 0-for-7 in six games while Hudson was first on the disabled list. He started one game in that stretch, May 8 against the D-backs.
In 28 games with Tucson, Forsythe was hitting .270 with five home runs and 24 RBIs in 111 at-bats.