Davies suffered a hamstring strain while playing for Bayern Munich in the Champions League on Tuesday, leaving the field in distress during their 6-1 win over Atalanta.
The 25-year-old only returned to action in December after recovering from an anterior cruciate ligament tear sustained in March 2025.
Canada face Iceland on March 28 and Tunisia on April 1 as part of their preparations for the World Cup, which they are co-hosting with the United States and Mexico.
"It'll probably be two-three weeks before he's back again," Marsch told TSN Sports.
"He's probably not going to be with us for March, which is okay. We'll probably leave him there in Munich and make sure he gets himself fully fit and fully back to 100%, and I'm confident he will do that.
"It's not easy when you come back from these long-term injuries ... We just need to take the appropriate steps to make sure that we don't have anymore setbacks."