Stones is on the road to recovery after undergoing surgery for ankle ligament damage sustained in Everton's 2-1 loss at Manchester United last month.
The 20-year-old English centre-back is progressing well and there are some suggestions that he may return ahead of schedule, but Martinez dismissed talk of a comeback before the New Year.
"The surgeon and the specialist have been very, very pleased. I think they've been quite surprised how quickly he is recovering," said the Spaniard.
"We need to be careful, though. The second half of the season is going to be really demanding and we want John to be fully fit and ready to cope with that.
"What we don't want is for him to come back for one game and then get in a position where his ankle isn't fully recovered and he needs more recovery time.
"He's doing well, though. He's walking around [Everton's training base] Finch Farm with no protection. He's ready to step up his individual programme and it's exciting for the turn of the year to see when he'll be ready.
"We don't know the date at the moment but I'd say sometime in January he'll be able to join the group which is incredible news."
