The league will not release the details of the discipline or the amount of the fine, the source said, confirming a story first reported by The Washington Post.
Umpire Phil Cuzzi called Jayson Werth out in a close play at first in the ninth inning of Thursday night's 1-0 loss to the New York Mets. Replays showed that Mets first baseman Daniel Murphy's foot came off the bag and that Werth was safe.
After the game, members of the Nationals' team argued with the umpires. Rizzo, who was unavailable for comment before Monday night's game at Milwaukee, said last week that the incident didn't have anything to do with the close play in the ninth inning.
The source said the league now considers the matter closed.