The Manchester United forward was lying on the ground following a foul when Williams kicked the ball into the back of his head during Sunday's Premier League match at the Liberty Stadium.
United manager Sir Alex Ferguson said Van Persie was "lucky to be alive" after the incident in the 74th minute of the 1-1 draw.
Martinez, who managed Swansea before joining the Latics in 2009, does not believe Williams acted out of malicious intent, and said: "I signed Ashley Williams for Swansea and I know his character inside out. I can guarantee you without even looking at the incident that he is not a nasty footballer."
He added: "He is a winner and fully committed, a leader and a captain, and I don't for one second doubt that he did not do that on purpose.
"You see the incident and it is a very, very dangerous situation. If you see one of your players with a bang on the back of the head it is really dangerous and it can have bad consequences. You can understand that.
"It is an action of the game. He can show frustration - it is an emotional game and it is very unfortunate that it hits Van Persie in a part of the body where he could have been hurt heavily, and you don't want to see that.
"But from my point of view, I know Ashley Williams really well - when you sign a player you find out about a player and I can guarantee you he is not the type of footballer who would do that on purpose."
Liverpool boss Brendan Rodgers, who was Williams's manager at the Liberty Stadium until he left in the summer, felt the issue had been blown out of proportion and was an unintentional mistake by the defender.
"I think more has been made of it than what it actually was," Rodgers said.
"When you slow it down and look at it 20 times it does not look good for Ashley.
"But I know the player well and it is just that split-second when you can see he is trying to clear the ball and unfortunately hits Van Persie right on the back of his head.
"Of course, it looks dangerous but knowing Ashley he won't have meant it, knowing his character that won't have been intentional."
Ferguson, who has called for Williams to be banned by the Football Association, looks set to escape punishment himself for comments he made about referee Michael Oliver.
The Scot was angry that Oliver allowed Swansea's equaliser to stand after Chico fouled Van Persie during the build-up.
Ferguson said: "It really it should have been a foul for us when the defender fouled Van Persie, but the referee has had one of those games. I know he is a young referee but, dear me, what a performance that was."