Atletico Madrid midfielder Hector Herrera is unfit for Mexico's friendly against Japan in Austria on Tuesday and will return to his club, while FC Porto winger Jesus "Tecatito" Corona is also a doubt for the match.
"It was determined that he should return to his club to continue his rehabilitation," read a statement from the Mexican national team.
Herrera has won a starting spot at Atleti in recent weeks and will be hoping to be back for Saturday's crucial La Liga game against Barcelona.
Martino said in a news conference on Monday morning that Corona is being monitored after picking up an unspecified knock against South Korea last Saturday.
"We'll wait for tomorrow [Tuesday]," said Martino. "As I said previously, we won't take risks with any footballer, and [Corona] is in that group of players."
Monterrey center-back Cesar Montes will also miss the match with groin injury and has returned to his Liga MX side.
Martinez won't be making many changes from the game versus South Korea, in line with what he has done in previous international breaks.
"The idea for tomorrow's game will be similar to the last one, without many changes from one game to the other," said the Argentine. "There will be some changes, other players will start again and I'll look to give minutes to others like I did the other day with [Orbelin] Pineda and Uriel [Antuna], who played around 35 minutes."
Martino stressed that it is normal for players not to feature in international football, but that it's part of being called into and competing for a place in the national team.
"In these types of tours there are players that feature more, others less and others that don't play," he said. "They are the game rules, there's no possible solution, unless FIFA tells us we can play with 15 players each game."
The Mexico coach is expecting a tough game against a Japan squad made up exclusively of players from European club teams.
"I think we are facing a very dynamic team, with very good individual technique, very tidy in playing out from the back and with individual talents, especially from midfield up, that are very unbalancing," said Martino. "In our case, we want to continue to consolidate an idea, regardless of the tactical set-up that we are going to use, to continue our way of playing, which is the one we adopted two years ago and try to sustain."
Mexico's record under Martino currently stands at 18 wins from 21 games, with the match in Graz El Tri's final one of a disrupted 2020.
In other Mexico-related news, El Tri's Under-23 manager Jaime Lozano said in a news conference on Monday that he heard men's Olympic qualifying could be played in a bubble in the United States, although he stated his preference is to play it in March in Guadalajara as originally planned.
