The Wales international made a clearance just a few steps away from the Dutchman in the 1-1 draw between the two sides on Sunday, powerfully striking the 29-year-old on the back of the head with the ball while he was on the ground.
Van Persie was furious and Old Trafford boss Sir Alex Ferguson suggested that the former Arsenal star "could have been killed" after the game.
But Martinez, who signed Williams while in charge of Swansea in 2008, insisted that the collision was unintentional.
"I know the character inside out and I can guarantee you, without looking at the incident, that he's not a nasty footballer," Martinez told reporters. "He's a winner and he's fully committed and he's a leader and a captain but I don't know for one second ... I doubt that he did that on purpose."