Rodriguez was scratched from Thursday night's game against the Cubs after sustaining the injury in batting practice. He is hitting .214 with two home runs and 19 RBI this season, and has thrown out 10 of 22 attempted base stealers. The move is retroactive to July 7.
Rodriguez termed it a "mild" injury, and said he expects to return as soon as he is eligible to come off the DL.
"For the next six or seven games I'll be a cheerleader in the dugout," he said.
Washington manager Davey Johnson said the team was taking no chances with the 39-year-old catcher.
"It is something you don't mess with," Johnson said. "Once you have a little strain of the oblique, if you continue playing you can really make it bad, and we don't want to do that here. He's too valuable to this ballclub."
The Nationals recalled catcher Jesus Flores from Triple-A Syracuse. Flores has played in two games with the Nationals this season, going 1 for 2. He batted .234 with five homers and 30 RBI in 56 games at Syracuse.
The team also announced right-handed pitcher Cole Kimball, who has been on the disabled list since June 10, will undergo surgery next week in New York to repair a torn rotator cuff in his right shoulder. Johnson said he expects the surgery to be season-ending.
Kimball was 1-0 with a 1.93 ERA in 12 appearances for the Nationals.