Gaudin went on the DL on April 27 because of inflammation in the shoulder, and he isn't traveling with the team on its road trip, which ends Thursday in Atlanta.
Manager Jim Riggleman said the reliever will need a Minor League rehab stint, which has not been scheduled.
Gaudin, 28, was signed as a Minor League free agent over the winter and made the team in Spring Training. But he had a 6.48 ERA in 10 appearances during April and had eight walks in 8 1/3 innings.
Right-hander Henry Rodriguez came off the DL when Gaudin went on, and Rodriguez will keep a spot. The Nationals must also continue to carry right-hander Brian Broderick or offer the Rule 5 selection back to the Cardinals.
"He's just got that general wear-and-tear soreness that doesn't appear it's going to be anything extremely significant," Riggleman said of Gaudin. "But he needs to go pitch some rehab assignments before we see him."