The England player accused Jesus Gil Manzano of "corruption" in a video that appeared to be taken in the tunnel following the game on 5 May.
Hammers boss David Moyes and defender Aaron Cresswell were sent off in the 1-0 defeat in Frankfurt. Moyes has been banned for one game.
Rice will miss both legs of West Ham's Europa Conference League play-off in August.
"Ref, ref, it's so poor, all night, it's so bad," Rice shouted at the Spanish official in the video. "How can you be that bad, honestly? You've probably been paid."
West Ham confirmed at the time they would not take any action against Rice. Moyes said: "If Uefa punish him that's down to them, but not on my watch."
Source: UEFA
The Hammers have been fined £1,500 because their fans used fireworks at the game in Frankfurt, while the hosts have also been punished.