The team announced earlier Saturday that Eaton had been placed on the disabled list with what was initially diagnosed as a left knee strain.
Fox Sports was first to report that Eaton had a torn ACL.
Eaton suffered the injury in the ninth inning of Friday's 7-5 loss to the New York Mets on a bang-bang play at first base. He hit a roller to the left side of the infield and just barely beat the throw to first. After reaching the bag, he collapsed in a heap as the crowd at Nationals Park fell silent.
Nationals manager Dusty Baker had said earlier Saturday that he hoped the injury was "not as serious as it looked."
The 28-year-old outfielder, acquired in a blockbuster December trade with the Chicago White Sox, is hitting .297 with a .393 on-base percentage.
Michael Taylor, considered the everyday center fielder before Eaton's acquisition, took his spot in center Friday night and is expected to see the bulk of playing time going forward.