Dobbins said he plans to appeal.
"It was a lot of zeroes in that picture," he said. "My assessment is (it's) is way too high and I feel like I didn't do anything wrong. I'm not a dirty player. I really can't do nothing but appeal it at this point."
The hit came in the second quarter of Houston's 13-6 win on Sunday night when Dobbins hit a scrambling Cutler after he threw a pass.
Cutler was past the line of scrimmage and called for an illegal forward pass on the play, and Dobbins was flagged for unnecessary roughness.
"I'm definitely disappointed," Dobbins said. "I didn't know if he was going to run the ball or if he was going to pass the ball. I felt like he was past the line. I just went and tried to get a clean hit on him and it just didn't work out, I guess. I looked at the film and it looked like I got a little helmet-to-helmet, but I definitely didn't try, though."
Houston defensive end J.J. Watt had a simple reaction when he heard about the fine.
"That's a lot of money," Watt said, shaking his head.
Cutler remained in the game for the rest of that series and threw an interception. He started experiencing symptoms at halftime and did not return.