The second baseman initially suffered the injury while making a throw during the team's loss to the Cardinals on Friday.
After making the playoffs three straight seasons, the Pirates missed the postseason in 2016 and are in last place in NL Central this year.
Koda Glover said he should have told the Nats he hurt his back in the shower, but he didn't "and now my back's in pretty bad shape."
Villar suffered a lower back strain in Friday's win over the Diamondbacks and needed to be carted off the field.
Chris Sale tossed seven innings, gave up three runs and struck out seven, finally getting that elusive win over Justin Verlander.
Giancarlo Stanton took a 95-mph fastball off his wrist in the first inning of Saturday's game, but avoided major injury.
Sale got his first win over Justin Verlander in six tries and the Mets welcomed back Yoenis Cespedes in a big way.
Pirates right-hander Jameson Taillon has not pitched for the Pirates since May 3 after being diagnosed with testicular cancer.
The St Louis Cardinals ended a seven-game skid with a 3-2 win over the Philadelphia Phillies in MLB action on Friday.
The Cardinals entered Friday night's game against the Phillies losers of 17 of their last 22 games and a reassigned coaching staff.