The Swedish superstar was handed the punishment after hurling himself theatrically to the turf in the 23rd minute of Galaxy's 3-1 defeat to the Crew on Wednesday.
The incident occurred after a collision with Crew goalkeeper Zack Steffen.
Crew midfielder Pedro Santos was also found guilty of simulation/embellishment during the game. Santos was also fined.
Ibrahimovic has been in superb form for the Galaxy this season, scoring nine goals in nine games. He is second in the MLS goalscoring charts behind Los Angeles FC's Carlos Vela.
Galaxy, who missed the playoffs last season, are second in the Western Conference standings, two points behind leaders LAFC.