The league's disciplinary committee said it had levied the fine "for violating the league's policy regarding hands to the face/head/neck of an opponent."
Miami's Ian Fray was fined an undisclosed amount for the same infraction.
It was late in stoppage time of a testy contest when Messi approached the centre circle to confront Sullivan while the ball was in play in another area of the field.
After a brief exchange, Messi took a swipe at Sullivan, who then squared up to the Argentine star in a fight-style stare-down.
Referee Filip Dujic, who had his back turned during the incident, arrived to separate the players but did not show either of them a card.
Dujic did send off Cavan Sullivan, younger brother and teammate of Quinn, and Miami's Italian midfielder Yannick Bright after their stoppage-time scuffle in Miami's penalty area.