Harper, 21, injured his hand during a head-first slide into third on a bases-clearing triple in Friday's victory over San Diego.
He stayed in the game for an inning before being replaced.
"I slid into the bag and I caught it a little bit," Harper said about his thumb after that game. "Went into the dugout, swung a couple in the cage, felt fine. Went out to the outfield, it swelled up a little bit. ... So I got in and got some treatment on it."
The extended loss of Harper is a significant blow to a Nationals roster already riddled with injuries to key players, among them catcher Wilson Ramos, third baseman Ryan Zimmerman (both with hand injuries) and starting pitcher Doug Fister (back).
Harper missed 44 games last season, his second in the majors, with a left knee injury. He was injured in mid-May when he slammed into the right-field wall at Dodger Stadium.
He is not the first star player to suffer a similar injury recently.
Los Angeles Angels slugger Josh Hamilton is out with the injury as well, and Boston Red Sox second baseman Dustin Pedroia played through it all of last season before having surgery in November.
All three players suffered the injury sliding into a base.
Information from The Associated Press was used in this report.
Sources: Harper To Have Thumb Surgery
The "Baseball Tonight" crew breaks down the impact of Bryce Harper's thumb injury on the Nationals and Harper himself.