To fill the roster spot, the Angels called up Alexi Amarista from Triple-A Salt Lake.
Bourjos injured his hamstring while rounding second base on an eighth-inning RBI double against the Mariners.
"It didn't really respond well," said Bourjos of his hamstring, according to the Los Angeles Times. "It's frustrating. It felt really good (Thursday) morning. It stinks to sit here and watch, but that's where I'm at right now."
Bourjos' DL trip means that prized prospect 19-year-old Mike Trout will remain in the big leagues a while longer. Trout was first called up July 8, but manager Mike Scioscia made it clear that the starting job still would belong to Bourjos.
"It is Peter's job when he comes back," Scioscia said after Trout was called up. "He's been playing better defensive center field than anybody in the league. We want Peter back in that lineup."
Bourjos is eligible to come off the disabled list July 23.
"He's making progress, but not enough to where we project him playing this weekend or the beginning of next week," Scioscia said, according to the Times. "The medical staff has drummed into our heads that hamstrings are different animals.
"If you're going to determine when a guy is going to be ready, it's better to (bring him back) three days later rather than three days sooner. Peter's speed is critical to what he does and to the team. We want him to get strong for next Saturday."
Information from The Associated Press was used in this report.