Messi limped out of Barca's trip to Real Betis earlier in November, and Martino could not allay fears for Barca fans that the attacker's return date is still unknown almost a fortnight on.
"I cannot be precise, I don't want to say one and later be wrong," said Martino, when asked about a return fixture.
"It will be at the end of the month and the beginning of December.
"The procedure will be that, what was decided by the club, it still always stands with the permission of Barcelona and its doctors.
"It's true that there is communication with AFA (Argentine Football Association) and with the doctors of their national team but anyway it's something that Barcelona will deal with.
"It's something that involved all those are worried about this Leo's situation even himself.
"So this is what we decided as the best to allow him to come back in the best way for the next year."
After the final date of Ballon d'Or votes to be accepted was pushed back two weeks to November 29, Martino said it was still a fait accompli Messi would win his fourth consecutive award.
"It's a waste of time thinking if it's a good thing to extend the time to vote for the Ballon d'Or," he said.
"For me the best player in the world is Messi and apart from that, everything is OK."
On upcoming opponents Granada, who Barcelona will welcome to the Nou Camp on Saturday, Martino said the league's eighth-placed side must be respected on their away form this season.
Lucas Alcaraz's men have recorded back-to-back road victories over Elche and Levante - both 1-0 results - and have 11 points from six trips in La Liga.
"This will be a tough match for that who Granada represent and for the way they're playing away this season, getting better results as a visitor and I think that the highest difficulty will be there," he said.
