Martial has found himself under fire following another woeful performance in United's goalless draw with Wolves at Old Trafford on Saturday night.
The Frenchman has been leading United's attack in the absence of Marcus Rashford, but looks lost in the lone striker role.
Martial, who cost United £50m from Monaco in 2015, has scored just once in his last six games and that came in the 6-0 drubbing of League One strugglers Tranmere in the FA Cup.
Solskjaer admits Martial, 24, has been flogged to death and needs a rest - but insists his work rate and attitude have been first class.
The United boss said: "He's giving us everything. He's been asked now to play - I think he's started the last eight games this month, and he's running probably 20 per cent more than what he did when I came here.
"That shift, and that goes with all the other players as well, it's not just mental robustness and tactical, it's that physical effort we've had to work with, because they are making strides.
"We'll give him more support and give him rest when he deserves it, because he's been asked to play too much as well, especially now when Marcus is injured.
"As a striker, if you don't just get there in that split second, that's a big, massive difference. I've praised him, I've sat down with him and I'm delighted with him.
"I know that he's tired, but he's never ever, how do you say it, dodged a training session. He's training, he's available for every game, so I'm delighted with the boy."
United, meanwhile, have no issues with Rashford's trip to Miami to watch last night's Super Bowl, despite him taking a seven hour flight to Florida while suffering from a double fracture of his back.
It is understood England boss Gareth Southgate also attended the Super Bowl and combined it with a leading coaching convention.