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.
"Maynor is a strong man and very fit. We will support him as much as we can."
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.