The on-loan Arsenal midfielder had to be carried off on a stretcher after a challenge from Everton forward Kevin Mirallas in Wigan's 3-0 FA Cup quarter-final win at Goodison Park on Saturday.
Miyaichi has been restricted to just seven appearances during his loan stint due to injuries and Martinez fears he will be sidelined again for a long spell with serious ligament damage.
"It was a terrible challenge. We are waiting on the scan but we are not very positive on it," he said.
"We think it will need a long recovery period and maybe he will even need surgery. We need to be a little bit expecting the bad news.
"He is very fortunate he has not got a broken leg because of the nature of the challenge.
"We feel he ruptured the ligaments. We will have to wait and see but he doesn't seem to have an opportunity to finish the season."
Callum McManaman limped off after scoring the second goal against Everton, but Martinez is hopeful that his ankle injury will only sideline him for a maximum of 10 days.
Martinez said: "Callum McManaman is recovering well and probably it is more a matter of a week - five days to 10 days - that he is going to be out.
"We will see how he recovers day by day. The ankle is swollen but it is more of a normal injury."