Messi, whose former Barcelona team-mate Jordi Alba was also forced to leave Wednesday's game early due to injury, missed Miami's 5-2 loss at Atlanta on Saturday due to fatigue and sat out Argentina's match against Bolivia last week.
Martino said they would evaluate the injuries to Messi and Alba in the coming days but added they would definitely miss Sunday's game against Orlando City and were in doubt for the Cup final next Wednesday against Houston Dynamo.
"There is no chance they will be there on Sunday. I know we have a final to play but they won't go near the pitch if they can't play," said Martino.
The coach added that Messi had been carrying an "old injury".
"The scans he had with the national team, they didn't show any injury. We still saved him to be safe," he added.
"We don't think he has a muscular injury. That's also from a conversation I just had with him. But we have to continue being careful. And we'll look at it the next few days."
Miami have yet to lose with Messi on the field since signing him in July, a run that includes a triumph at last month's Leagues Cup.