League sources told ESPN's Adam Schefter that the fine is $975 more than the minimum based on the NFL's fine schedule.
Manziel extended his middle finger after a third-quarter incompletion in front of Washington's bench during Cleveland's 24-23 loss Monday night.
Manziel said at the time that he had "words exchanged" with the Redskins.
"I felt like I did a good job of holding my composure throughout the night, and you have a lapse of judgment and slip up," Manziel said after the game.
Manziel can appeal to have the fine reduced because it is more than 25 percent of his weekly salary of $24,075, according to Pro Football Talk.
Manziel will enter the regular season as the Browns' backup quarterback after Brian Hoyer was named the starter on Wednesday.
"It does not sit well," Browns coach Mike Pettine said Monday about Manziel's gesture. "It's disappointing, because what we talk about is being poised and being focused. ... That's a big part of all football players, especially the quarterback."