8:05 AM PT -- A source connected to Savage tells us ... FOX investigated this claim and interviewed every possible witness. They also looked at video and never saw anything inappropriate on Savage's part. We're also told they couldn't find a single witness to verify the woman's claim.

The source called the allegation, "Absolutely 100% false."

Fred Savage allegedly attacked and harassed a female crew member on the set of the TV show "The Grinder," and she's now filing a lawsuit ... TMZ has learned.

The alleged incident went down in 2015 while Savage was working on the FOX show. We're told the woman, who worked in wardrobe, is claiming Savage had it out for her and created a hostile work environment -- including verbally dressing her down in front of other people.

We're told things came to a head when she was brushing dandruff off his clothing, while he was wearing it, he got pissed and allegedly "violently struck" the woman 3 times in the arm. The woman claims Fred had a rep for losing his cool with female crew members.

The crew member plans to sue Savage and Twentieth Century Fox for harassment, assault, battery and discrimination. We've reached out to reps for FOX and Savage, but no word back yet.