Boone, 35, suffered the injury in the eighth inning last Sunday against the Reds, while jogging to first base to pinch-run for first baseman Dmitri Young.
"It's a little embarrassing, but what are you going to do?" said Boone about the way he got hurt.
Before the injury, Boone was a valuable reserve, hitting .258 with five home runs and 17 RBIs this season. The Nationals are hoping that he will be back by July 22, when they play the Giants in San Francisco.
"Realistically, I wasn't going to be back by this weekend. When the time is up, I'll be ready to go," Boone said. "With a strain, you never know. It's new to me. We are going to work to get it right and hope to be ready when the time expires."
This is Orr's second stint with the Nationals this season. He went 2-for-11 (.182) in seven games. Orr batted .275 (78-for-284) with two home runs and 33 RBIs in 73 games with Columbus. He leads the International League with 11 triples.
According to a baseball source, Orr had a 6 p.m. ET flight to Washington and was expected to be late for Thursday's game against the Diamondbacks.
In other news, third baseman Ryan Zimmerman took batting practice for the third consecutive day and continued to look good with the bat. According to manager Manny Acta, Zimmerman will have another session on Friday and will have breaking balls thrown to him.
General manager Jim Bowden said if things go well, Zimmerman could start a rehab assignment sometime next week. The team is hoping that he is back playing in a Major League game by late July.
"He's doing great," Bowden said. "We're very pleased with his progress. He had a really good day again today. No problems with the bat, getting better every day, great on the field. Hopefully, he can go on rehab by early next week."
First baseman Dmitri Young continues to have back problems and hasn't been able to take batting practice. However, he was able to play in the first three games against the Diamondbacks.
Young has had back problems since Sunday.
Bill Ladson is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.