The Honduran full-back suffered the setback at the weekend in the victory against Burnley at Turf Moor.
Martinez said: "Maynor has had a second scan and we now know he has a tear in the medial ligament in his left knee. It is not as bad as we feared at the beginning. He will be out for between six and seven weeks."
He added: "Maynor is a strong man and very fit. We will support him as much as we can.
"It is a big blow when any player is injured as we have a small squad and everyone has a massive role. But it is part of football and you have to cope."
Wigan could also be without Paul Scharner at Portsmouth on Saturday as he has a hamstring injury, while goalkeeper Chris Kirkland remains troubled by a dislocated finger.
Meanwhile, Martinez has phoned Sir Alex Ferguson to explain remarks attributed to him in a Spanish newspaper.
Martinez has also contacted Steve Bruce, Sam Allardyce and Rafael Benitez after they were all implicated in the article.
The Spaniard felt the need to clear the air after categorically denying he suggested the Football Association are afraid to punish Manchester United boss Ferguson.
Martinez said: "Those managers have probably been in this situation and know how things work. I have had a lot of support in that respect. To speak about other managers you need to win the league. But it is not in my nature to be outspoken."