McGrath was one of three players taken to hospital from the MCG on Friday night, along with teammate Archie May (ribs) and Tigers forward Tom Lynch (throat).
The Bombers also lost Sam Durham (concussion) and Matt Guelfi (hamstring) in their 10.14 (74) to 7.14 (56) defeat, which sent them crashing to last place on the ladder.
McGrath was discharged from hospital early on Saturday morning after scans confirmed the fracture, and will have surgery in the coming days.
He will miss Essendon's crunch clashes with West Coast (away), Carlton and Melbourne ahead of their mid-season bye.
Guelfi will also miss at least three games and Durham at least one, while May has been cleared of serious damage and is set to play against the Eagles at Optus Stadium on Sunday.
Jye Caldwell pulled up sore with a leg injury and will be monitored in the coming days.
AFL-listed Will Setterfield and Elijah Tsatas were pulled out of Saturday's VFL match in case they are required to play against West Coast.
Speaking after the loss to Richmond, Essendon coach Brad Scott said McGrath was "terrible" after he took an accidental elbow to the mouth and lost a tooth.
"He's got a pretty noticeable crack that you can see and feel in his jaw," Scott said.
"It's not a good one. I'm not diagnosing it, it's just like that one's pretty obvious.
"Sometimes you can put a plate in it and they can come back pretty quickly, but I'm not sure on that one."
Essendon lost Durham and Guelfi in the opening 15 minutes and McGrath before halftime, but fought bravely in the second half.
They controlled play in the third quarter without capitalising, kicking 1.6 for the term, and managed to cut a 22-point margin back to just seven points when Caldwell kicked the first goal of the last quarter.
But the Tigers steadied with the last two goals of the match to leapfrog their opponents into 17th position on the ladder.
"It would've felt like a steal and that's the pleasing thing, that there's fight there," Scott said.
"But there's also a scoreboard and at the end of the day that's really all that anyone cares about."
Bombers midfielder Darcy Parish won the Yiooken Award as best afield in the annual 'Dreamtime At The 'G' centrepiece of Sir Doug Nicholls Indigenous Round.
He had 40 disposals and nine clearances in a strong display, and was then jeered by Richmond supporters in the 78,815-strong crowd when accepting his prize.
Former Brisbane Lions hard-man Scott laughed off the incident, likening it to Collingwood's Nathan Buckley claiming the 2002 Norm Smith Medal.
"Richmond fans, when you win, you expect your player to win the medal don't you?" Scott said.
"I've got visions of Nathan Buckley in a game I played in taking a medal off his neck after a grand final.
"No, I thought Parish played well. I'm not a big one for individual medals anyway."
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