In the bottom of the fifth inning, Dukes hit a slow roller to Braves third baseman Chipper Jones, who easily threw out Dukes. Manager Manny Acta took Dukes out of the game after the inning and replaced him with Willie Harris, who will see more playing time while Dukes is sidelined.
Dukes has had hamstring problems for several weeks and missed a handful of Spring Training games.
"It's not getting any better by me going out there and still trying to run on it," Dukes said. "I'm going to give it some time and let it heal properly so I can give 110 percent."
To replace Dukes on the roster, the Nationals recalled right-hander Chris Schroder from Triple-A Columbus. Schroder, 29, went 0-2 with a 4.09 ERA in nine Spring Training games.
Last season, Schroder went 2-3 with a 3.18 ERA in 37 games with the Nationals.
As for Cordero, he felt sharp pain in his shoulder during batting practice and immediately told the training staff. Cordero was given a cortisone shot and will rest for a few days.
"I felt sharp pain down my arm, but I didn't think anything of it," Cordero said. "I thought maybe it was kind of cold and I wasn't stretched out. It kept happening. Even during BP, when I was throwing the ball to left field, I could feel it."
Jon Rauch, who blew the save Sunday before getting the win after Ryan Zimmerman's walk-off heroics, will be the closer in Cordero's absence.
In other news, the Nationals signed infielder Ray Olmedo to a Minor League contract. He is considered insurance in case anything happens to one of the backup infielders such as Felipe Lopez.
Bill Ladson is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.