The Danish forward has been a regular this season under head coach Frank de Boer but, after limping out of Sunday's 4-0 win over AZ, tests have confirmed a tear in his muscle.
Fischer has made 35 appearances for Ajax in competitions this season, scoring seven goals, but he is now set to miss a large part of the remainder of the campaign.
"On Sunday in the match against AZ, Viktor Fischer sustained a tear in his left hamstring," a statement on the club's website read.
"The Danish forward has been ruled out for at least six weeks.
"In a few weeks he will have another test to see how the hamstring is recovering."
Fischer joins a growing injury list at the Amsterdam Arena, and the club do not expect Lasse Schone, Thulani Serero or Nicolai Boilesen to be available in the near future.
The statement continued: "Lasse Schone has a torn ankle ligament. He is recovering well, but will not travel to Salzburg (in the UEFA Europa League on Thursday), and the match against Feyenoord (on Sunday) will probably come too early.
"Thulani Serero flies to Salzburg but is not in the squad. The South African has been struggling with a groin injury and will continue his rehabilitation.
"Finally Nicolai Boilesen has a left hamstring injury and is therefore not available in the upcoming weeks."
Ajax are six points clear at the top of the Eredivisie, and will look to turn around a three-goal deficit in their Europa League last 32 clash with Salzburg on Thursday.
