The Toffees manager admitted he could not estimate just how long the England international would be sidelined, but said the initial signs are encouraging.
Martinez told the club website: "His knee has reacted really well to treatment.
"I don't know where the figure of five months [in the papers] came from but obviously the extent of the injury is a little unsure at the moment because we don't know how the next two weeks are going to develop.
"It's a medial ligament injury and we know that Ross, in terms of the power and the strength that he has in his body, he could easily react to treatment a lot better than other players.
"The length that Ross will be out is a little uncertain at the moment and it could be anything between the eight weeks that we mentioned or a little further. Until the end of the week, or probably the next 10 days, we won't know how the knee is progressing and how quickly Ross can be back.
"Obviously we are keeping an eye, very closely, on how that knee reacts and every time we have a real improvement we are checking that.
"At the moment his knee is in a brace and this is a very important period of rehabilitation, making sure that the ligament can be repaired in a good position. Obviously we are going to get further updates in days to come but we need to leave Ross alone and leave him to recover."
Martinez also confirmed that Seamus Coleman, who missed the game at Leicester on Saturday, is back in the reckoning for the game against Arsenal on Saturday.
"Seamus was fully fit from a medical point of view on Saturday and that was a real boost," Martinez added. "He has been working really well, and he was desperate to be part of the squad on Saturday.
"I think now it's fair to say that he's considered fully fit and ready to join the group and help the team in any game."