Team sources told ESPN's NFL Insider Adam Schefter that Washington is out for the rest of the season.
Washington went down on his only carry of the day when a defender rolled up on his right leg after a 6-yard run. Teammates said the bone broke through the skin, and it was visible on the field. Washington was helped off the field by two trainers and then taken away on a cart.
He was diagnosed with a broken right fibula and underwent surgery immediately after the Jets' 38-0 victory.
"That's unfortunate," coach Rex Ryan said. "It's obviously a severe injury, but hopefully he'll be joining us sooner than later."
Washington, who made the Pro Bowl last season as a kick returner, is also New York's second-leading rusher with 330 yards on 71 carries. He also has 15 catches for 131 yards and takes direct snaps when the team runs out of the seminole formation.
In his absence, rookie Shonn Greene excelled, carrying 19 times for 144 yards and two touchdowns. Greene, a third-round pick out of Iowa, had only eight carries for 31 yards coming in.
Starter Thomas Jones ran for 121 on 26 carries as New York finished with 316 yards on the ground. After gaining 318 yards rushing last week, the Jets became the sixth team to top 300 in consecutive games, and first since Buffalo did it in 1975.
"Anytime we have a game like that, you want to cherish and enjoy it, but it's kind of hard to do that with Leon's injury," Jones said. "I think a lot of the team is devastated. He's one of my best friends. He's a great teammate and a great person. From the time he left the game, every couple plays I kept thinking about him. I haven't stopped thinking about it, and my prayers are going out to his family."
It's the second major injury to a key player for the Jets in as many games. Nose tackle Kris Jenkins was lost for the season after tearing the anterior cruciate ligament in his left knee in New York's 16-13 overtime loss to Buffalo last Sunday.
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.