Quinn, who said he received a letter from the league on Wednesday, would not disclose the size of the fine, but a league source tells ESPN NFL Insider Adam Schefter the amount is $10,000.
A league source tells ESPN's Michael Smith that an MRI exam showed Suggs suffered a severe MCL sprain in his right knee from Quinn's block on Monday night. There is no definitive timetable for Suggs' return, but he is expected to miss at least the next couple of weeks, the source said.
Suggs' agent, Gary Wichard, told the Carroll County Times he fears his client could miss the rest of the season.
Quinn insists he was not trying to hurt Suggs and has apologized to him and the Ravens. He understands why the Ravens were mad and can appreciate them questioning his intentions.
"I can see why they'd be upset," he said. "But again, he wasn't even in my vision. I was trying to get to the ball. He cut across my face as I was already try to jump down for the tackle."
The Ravens were fuming over the hit. Quinn threw the chop-block at Suggs after an interception in the third quarter, rolling into his right knee.
After the game, Quinn said the chop-block came as he was trying to get at cornerback Chris Carr, who intercepted the football, and that he had no intention of hurting Suggs. But Ravens linebacker Ray Lewis said after the game that he thought Quinn should pay a significant fine for the hit.
"Heck yeah, it was a cheap shot, when you're running down and you're looking at the quarterback going at somebody's knees who doesn't even have the ball," Lewis said. "I want to see if he gets the same fine I got or even higher. Now this man [Suggs] is out four or five weeks because of some baloney like that."
Lewis was fined $25,000 earlier this season for a pair of hits in a game against the Cincinnati Bengals.
After the game, Quinn said he was sorry.
"I was trying to go for the ball carrier," he said. "Suggs came across at the last second in my vision. I would never wish that upon anyone. I was upset about it on the field. We worked out in Arizona together. I couldn't be any more sorry about that. That was never the intent. I'm sorry to Terrell and the rest of their team."
"You just don't do that," San Diego Chargers linebacker Shaun Phillips told ESPN's "First Take" on Wednesday, saying Quinn should be fined $50,000.
Wichard wasn't buying Quinn's explanation of how he came to hit Suggs.
"That cat should be fined as much as anybody is fined that hits the quarterback," Wichard said, according to the Carroll County Times. "That's ridiculous. I don't understand what he was trying to do. It was blatant. It's absolutely criminal. It's about as nasty as it gets.
"The guy had total control and went right for his knee. You can't call that an accident. It was premeditated. The quarterback zeroed in on Terrell's knee. That's absurd. The ball carrier was right in front of him," he said, according to the report.
Browns coach Eric Mangini believes Quinn was only trying to tackle Carr.
"Knowing Brady, he's a good person," Mangini said. "I don't think he would ever look to hurt someone deliberately."
Ravens coach John Harbaugh said Tuesday on his radio show that he doubts Quinn had malicious intent. But that doesn't change that it was an illegal hit, he said, according to The Baltimore Sun.
"There is no question that it's beyond the rules. It's absolutely illegal. I'm sure Brady knows that," Harbaugh said, according to the report. "I don't think for one second that he's trying to hurt Terrell Suggs. But he's got to be better than that in that situation. You can't let that happen."
Quinn isn't the first quarterback to have to pay up for a low hit. Brett Favre of the Minnesota Vikings was fined $10,000 for throwing a crackback block in a preseason game against the Houston Texans.
ESPN NFL reporter Michael Smith and The Associated Press contributed to this report.