With first-choice right-back Seamus Coleman struggling to overcome a hamstring injury, Hibbert is in line to start his fourth consecutive match for Everton.
Hibbert has been utilised against Swansea City, Liverpool and Krasnodar, but Everton's trip to Old Trafford is expected to provide the 33-year-old with his biggest test.
However, Martinez is confident Hibbert will be able to cope with the likes of Robin van Persie, Radamel Falcao, Angel Di Maria and Juan Mata.
"I'd have no concerns about using him at Old Trafford," said Martinez.
"For him to be able to play the games he has against different types of opposition, tricky wingers with different ways of playing, he has done very well.
"That's why it's so important this season to have a strong squad. You need reliable characters like him."
Martinez added: "It's so important to have someone like Tony around the place.
"First of all, forget about playing, his influence is huge on the other lads. But then when he's on the pitch he brings that experience to everything. He's always ready to perform."
'I won the World Cup and I said to myself, I've done it all, I need to keep feeling emotions': Raphael Varane opens up on why he had to leave 'indescribable' Real Madrid for Manchester United
'When I see Phil Foden play, he just seems like a shy lad - that holds him back a little bit. He has been tried in every position, but he just hasn’t performed': Ex-England star makes bold claim about Manchester City man
