The incident occurred midway through the second period of Thursday's 4-3 overtime victory over the Sharks. Tkachuk, who was hit with a major and a game misconduct, accused Davison of diving.
"No I'm not worried because I know what I did," Tkachuk said after the game. "It wasn't as bad as everyone thinks. The guy embellished it."
Tkachuk was suspended four games in February for a cross-check on Wes Walz of Minnesota. Under the terms of the collective bargaining agreement, the 31-year-old Tkachuk will forfeit $487,804 of his salary.
"Mr. Tkachuk is a repeat offender who used his stick in a dangerous and inappropriate manner," said Colin Campbell, the NHL's director of hockey operations. "Blows with the stick to the head continue to be unacceptable."
Tkachuk will miss Saturday's game at Los Angeles, Sunday's contest at Anaheim and a visit against his former club, Phoenix, on Wednesday.