Martinez has not played since the 4-3 defeat to Bayern Munich in the Champions League last week, missing games against Burnley and Crystal Palace in the process.
The 25-year-old first suffered the injury in April against Sevilla in the Europa League which curtailed his debut season in England.
He has suffered a recurrence of the problem in the early part of the new campaign and has been playing through the pain recently.
“Lisandro Martinez will be out of action for an extended period due to an aggravation of the foot injury he suffered in April,” the club said.
“The Argentinian defender experienced the setback in our Premier League game against Arsenal earlier this month.
“Martinez bravely continued playing for the following two games against Brighton and Bayern Munich.
“But it has now been determined that he needs a period on the sidelines for recovery and rehabilitation. Assessment is ongoing to decide next steps.”
At a news conference on Friday, manager Erik Ten Hag said: "It is very sad, for him and the team, because he was not 100% fit.
"I think it was a big difference, the Licha Martinez in the last games and the Licha Martinez we have seen in the last season."
Martinez could be missing for more than two months with the injury.
