Cordero was examined by Dr. James Andrews in Birmingham, Ala. He had complained of a "click" in his shoulder after pitching one inning in Atlanta on Monday.
"We were very pleased," Nationals general manager Jim Bowden said before Wednesday's game against the New York Mets. "Dr. Andrews was encouraged."
Cordero will begin a program to build up his shoulder strength designed by Andrews, Bowden said. Cordero planned to rejoin the team Wednesday night.
Cordero came off the 15-day disabled list Saturday, after missing 12 games due to tendinitis in his shoulder. Cordero has pitched just three innings in four games this season, with no save opportunities and no decisions.
Cordero has been the team's closer since the middle of the 2004 season, when the organization was still in Montreal. His 128 career saves are 24 behind Jeff Reardon for the franchise lead.
"He was making a lot of progress on the mound," manager Manny Acta said. "I was ready to -- one more outing -- put him back in his old job."