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.
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.
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