Video footage showed Messi approach the coach and grab the back of his neck, causing him to pull away from the eight-times Ballon d'Or winner after the 2-2 draw in Miami.
The fine was imposed by the MLS' Disciplinary Committee on Tuesday.
The top-flight North American league also fined Messi's teammate Luis Suarez on Tuesday for violating the same "face/head/neck of an opponent policy" during halftime, when he pinched the back of Norwegian defender Birk Risa's neck.
Miami are due to play Sporting KC later on Tuesday in the CONCACAF Champions Cup.