The actor is alleged to have threatened the 78-year-old on several occasions, reports TMZ.
Teddy Joye Hicks Gibson married the actor's father Hutton Gibson in 2001, and has said that she fears for her safety in new court documents.
She claims that Gibson and his sister Maura often clash with her due to her disapproval of their controversial medical treatments for their ailing father.
The court papers claim that in October 2011, Gibson "began yelling and saying, 'f**k this and f**k that' while levelling other extremely offensive language at [her]".
In January 2012, she added that he once "got up, looking wild and began yelling at [her] in a very loud and terrifying voice".
"Mel was so upset and screaming so fiercely that I could see his face turn red," she alleged.
"[In May 2012] Mel became incensed and began acting like a wild man. He was so close that I could feel his spit hitting my face."
The order would mean Gibson must remain 100 yards away from her at all times, with a full hearing scheduled for next month.
Mel Gibson recently admitted that he has "a little bit of a temper" after a highly publicised rant against screenwriter Joe Eszterhas.