"It's not a two- or three-day thing, but hopefully it's recovered by six or seven days," Street said.
The Padres added left-handed relief pitcher Tommy Layne to the roster from Triple-A Tucson. He is in uniform and available for Saturday's game.
Street sounded mostly encouraged about his injury, noting that while it's the same calf that landed him on the disabled list last season and caused him to miss 35 games, that this latest injury is not nearly as serious.
"Same calf, different spot and a different severity level," Street said. "We wanted to make sure to avoid the same mistake twice. The risk isn't worth the reward."
Last season, Street had soreness in his calf leading up to the point where he suffered a severe strain in a game in Pittsburgh in August. He missed well over a month and didn't return until Sept. 21.
"Last year, when he suffered the injury in Pittsburgh, he felt discomfort and was able to play through it … then it got him," said Padres manager Bud Black. "… We decided to play it safe and get him healthy."
Street is 0-3 with 11 saves in 12 opportunities, but has a 4.43 ERA in 20 1/3 innings. He has also allowed seven home runs.
Black said that relievers Dale Thayer and Luke Gregerson will handle the late innings, but that Gregerson could "be the guy we turn to the most" in close games.
This is Layne's second stint with the Padres. He was recalled on May 24 and appeared in one game before heading back to Tucson. He was 1-3 with a 3.79 ERA this season for the Padres' top affiliate.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. Jamal Collier is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.