The team also reinstated right-handed reliever Joe Blanton from the 10-day disabled list.
Glover, 24, said he felt his back lock up on him while showering before Saturday's game against the Texas Rangers.
Glover admitted he did not notify manager Dusty Baker or the training staff about the injury until after he surrendered three hits and two runs in the ninth as the Rangers tied the game and forced extra innings. It was his first blown save since taking over as the Nationals' closer last month.
"I was taking a shower, bent over to get my body wash, stood up and had a little kink," Glover told reporters after Saturday's game. "With some issues I've had lately, I kind of pushed myself.
"I didn't want to take a day off. I've had three days off already, so I pushed the limits today, tried to pitch through it. And it's one of them things where it was out of my control and I should have said something early. I didn't and now my back's in pretty bad shape."
Glover leads all major league rookies with eight saves. He is 0-1 with a 5.12 ERA in 23 games this season. From May 13 to May 30, he recorded scoreless relief in nine straight outings spanning 8 2/3 innings pitched, converting all five saves along the way.
The hard-throwing Glover spent 14 games on the DL last month because of a hip strain, which was an aggravation of the torn labrum in his hip that forced the Nationals to shut him down last season.
"I'm tired of being hurt," Glover said. "Never been hurt before until last year, and ever since then, it just seems like something new keeps popping up every day."
Blanton, 36, returns to Washington's bullpen after missing 21 games with right shoulder inflammation. In one rehab appearance, with Double-A Harrisburg on Thursday, he Blanton tossed a perfect inning, striking out two batters.
Prior to being placed on the disabled list on May 17, Blanton was 0-2 with a 9.49 ERA in 14 appearances out of the bullpen. He was 7-2 with a 2.48 ERA in a career-high 75 games with the Los Angeles Dodgers in 2016.