It's the first large fine handed out by the NFL since it sent a video to the 32 teams emphasizing what hits would bring big fines and possible suspensions.
Sims, 25, is a repeat offender. He was previously fined twice for unnecessary roughness violations (Dec. 28, 2008 and Sept. 13, 2009) while he was a member of the Detroit Lions.
The fine was issued by NFL Executive Vice President of Football Operations Ray Anderson, who informed Sims that "further offenses will result in an escalation of fines up to and including suspension."
Hawkins' only catch in the game was for 5 yards in the third quarter.
Few penalties have been called for hits to defenseless players in the head or neck area since the crackdown.
The Associated Press contributed to this report