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Teddy Gibson, who married the actor's father John Gibson in 2001, filed for the restraining order in the Superior Court in Los Angeles.
A hearing is set for 25 July.
"Mel has sunken to new lows over the last year by committing several acts of domestic violence against his 78-year-old stepmother," the court papers state.
The petition accuses Gibson of screaming at his stepmother after she questioned his preference for medical treatments in the care of his 93-year-old father.
There have also been reports that Mel spat in Teddy's face.
Divorce questions
John Gibson filed for divorce from his wife in June, citing irreconcilable differences.
In her filing, Teddy Gibson claims she does not know why and needs the restraining order to talk to him without Mel Gibson present.
In a sworn statement with the filing, Teddy Gibson claims there are "a lot of questions about (John Gibson's) filing of divorce against me, and (I) need to speak directly to my husband without Mel's interference so that I can make sure both he is OK and not being manipulated by Mel or into a course of action he does not wish to take."
A spokesperson for the actor had no comment on the request for a restraining order.
Anger issues
This new action is the latest against Gibson, 56, to highlight anger issues since he was stopped by a California police officer in 2006 for driving under the influence of alcohol and launched into a rant that included an anti-semitic statement.
More recently, he and former girlfriend Oksana Grigorieva waged a bitter custody battle over their infant daughter during which tapes of telephone messages surfaced in the media on which Gibson can be heard yelling and screaming at Grigorieva.
In March 2011, Gibson admitted in court that he slapped Grigorieva with an open hand during an argument, and he pleaded no contest to domestic violence - the equivalent of guilty in California.
He was sentenced to three years probation.
