The move was made retroactive to Tuesday, Aug. 16.
"We put him on the DL so we did not have the urge to push him," manager Bruce Bochy said, according to the San Jose Mercury News. "Or to have Willie go out there when he's not right. He wanted to try to get through it. Long term, it's the best thing for his career."
Giants trainer Dave Groeschner told the Mercury News that the team hopes to have a timetable for Wilson's return by Tuesday.
"We definitely expect him to come back, but not until we're sure he's feeling good," Groeschner told the newspaper. "He wants to pitch. That's awesome. But we've got to make sure he's feeling good."
The team recalled right-hander Steve Edlefsen from Triple-A to take Wilson's roster spot.
Wilson hasn't pitched since reporting pain in his elbow after blowing a save last Monday. He gave up three runs in the ninth as the Braves pulled out a 5-4 victory.
Wilson flew to Pensacola, Fla., last Wednesday to get his elbow checked out by Dr. James Andrews, who performed major elbow surgery on the reliever eight years ago.
Andrews found no major problems, sending Wilson back to Atlanta with a recommendation of rest and treatment. But he will continue to monitor Wilson's progress by telephone.
Information from The Associated Press was used in this report.