Both Rivet and Dandenault underwent MRI tests following the team's 3-2 shootout loss to the Ottawa Senators Saturday night.
"We're confident that Craig will able to play Tuesday," Canadiens coach Guy Carbonneau said Sunday. "Mathieu's case seems more worrying to us. He could have to skip (Sunday's game)."
Rivet injured his foot blocking a shot during a third-period Senators power play, while Dandenault hurt his thigh fighting off a check.
They were the only two Canadiens players to play all 82 regular season games last year.
Rivet is something of a ironman for the Habs, having missed only two games over the past four seasons.
"He is already feeling better," Carbonneau said Sunday.
But despite Carbonneau's optimism about his injured defencemen, it looks like Mark Streit will suit up for the first this year sometime this week.
Carbonneau indicated that the Swiss defenceman would see action either against the Flames or in Chicago on Wednesday.
"I didn't want Mark to stay inactive for too long," Carbonneau said. "He was left out because of the arrival of (defenceman) Janne Niinimaa, but he took it like a professional."
Streit, who had a solid training camp, isn't discouraged by the team's surplus of defencemen.
"There's nothing I can do about it," the 28-year-old defenceman said. "I know that things can change rapidly. So I force myself to stay positive and to be ready for when they need my services."
Streit, who captains the Swiss national team, played 48 games last year, scoring two goals and nine assists to go with a plus-minus rating of minus six.