Martinez will make only his third Arsenal start at the Constant Vanden Stock Stadium, with his previous senior appearances for Arsenal having come in the League Cup two years ago.
The 22-year-old Argentinian has been pressed into UEFA Champions League action as a result of Wojciech Szczesny's suspension and an aggravation of David Ospina's thigh injury.
Wenger insists he has full confidence in a goalkeeper who played 15 games on loan at Championship side Sheffield Wednesday last season.
"[I am] extremely confident because he has experience from Sheffield last year and when he played for us he did very well. I have no special worry about that," said Wenger.
Martinez conceded five goals when he last played for Arsenal, in a dramatic 7-5 win over Reading.
"He is two years older now and has a good experience," Wenger added. "He has grown in stature as well."
Ospina, a close-season arrival from Nice, is facing a lengthy lay-off after suffering a recurrence of the thigh problem he suffered at the World Cup.
Wenger revealed Szczesny's dismissal in Arsenal's previous Champions League group game against Galatasaray had played a major role in Ospina's latest setback.
"I had to bring Ospina on against Galatasaray without warm-up, without being prepared, and he had a recurrence of that injury," explained the Frenchman.
"That means he is out for two to three months. We have to be really careful because he has a recurrence of a thigh injury that's very difficult."
