The incident occurred during the dying minutes of the Cats' loss to the Kangaroos at Etihad Stadium on Friday night.
Enright didn't apply much force with his foot to Thompson's leg but his action was enough to draw the ire of one of Thompson's teammates, who ran in and remonstrated.
The MRP charged Enright, who has never been suspended during his 261-game career, with misconduct.
His initial penalty was a $1200 fine, but he can reduce it to $900 with an early guilty plea.
Enright's Geelong teammate Josh Caddy has also copped a $900 fine for making negligent contact with an umpire.
Gold Coast midfielder Dion Prestia faces a $1950 fine for pushing West Coast's Andrew Gaff into an umpire during the Suns' narrow loss to the Eagles at Patersons' Stadium on Saturday night.
Brisbane Lions defender Mitch Golby is the only player suspended after the MRP's review of round 19.
Golby has been cited for striking St Kilda's Tom Curren in an off-the-ball clash at the Gabba on Saturday night.
The incident was assessed as intentional, low impact and high contact.
Golby's initial penalty was a two-match ban, but he can accept a one-game suspension if he pleads guilty.
The match-day report laid against Gold Coast's Campbell Brown for engaging in rough conduct against West Coast's Blayne Wilson was thrown out.
The panel decided that Brown’s actions were a legitimate attempt to win possession.
