Pena said he wants to come back quickly.
"I need to work, and I'll work hard," said Pena, who hurt himself Wednesday during batting practice.
The 26-year-old outfielder was projected to be the starting left fielder for the Nationals.
"We were willing to give the guy the opportunity to get 500 at-bats, and now another year is going to go by and next year we'll probably be hearing the same thing about him," Nationals manager Manny Acta said.
Elijah Dukes becomes the likely starter in place of Pena.
Dukes was removed from Friday's split squad game against the Cleveland Indians in the third inning when he was hurt sliding into second base. He strained his right hamstring and is day-to-day.
Dukes said he's just happy to make the Nationals, and that starting is a bonus.
"I don't know what my role is going to be," Dukes said. "When he comes back, I'll probably be the fourth guy again, so we'll see what happens."
Last season Pena split the season with the Boston Red Sox and the Nationals. In 73 games with the Red Sox, Pena hit .218 with five home runs and 17 RBIs, but in 37 games with the Nationals, he hit .293 with eight homers and 22 RBIs. This spring, Pena was hitting .226 with one homer and four RBIs in 31 at-bats.