Tkachuk will sit as Calgary tries to end a three-game losing streak Thursday night in Montreal.
The play began when Martin came across the ice and checked Troy Brouwer into the boards, leading to a brief scrum. Giordano made Martin pay for his hooking penalty when his wrist shot from the point went through traffic and beat Andersen midway through the first.
Tkachuk was already considered a repeat offender after receiving a two-game suspension for elbowing L.A. Kings defenseman Drew Doughty a year ago in his rookie season.
Tkachuk speared Maple Leafs forward Matt Martin from the bench with 5:53 remaining in the first period of Wednesday's game.
"I just want to take it one game at a time, real important to be able to flip the page", Andersen said.
The 28-year-old Martin told reporters that he wasn't initially aware of the spear - "I did not feel it at the time" - but had watched the video and called it "child's play". "He'll learn over time", said Maple Leafs head coach Mike Babcock during Wednesday's post-game press conference.
"I thought it was a good hockey game, I look at how our team played start to finish I like our game", said Flames coach Glen Gulutzan.
"You can play with an edge for sure, I think he's an effective player, good player", said Martin.
Tkachuk is only two weeks removed from a one-game suspension for unsportsmanlike conduct stemming from an incident in a November 15 matchup with the Detroit Red Wings. "No reason for that stuff". Unlike the Martin incident, Tkachuk was given a five-minute major for spearing and a game misconduct on the play. "When you're sitting on the bench or the situation in Detroit.it's not really necessary".