The 27-year-old Algerian international winger was given a straight redcard by referee Mike Dean for a tackle on Phil Jones after just quarter of an hour of Monday's Premier League match with Manchester United.
United ended up scoring two second-half goals to win 2-0.
The decision incensed Hammers manager Slaven Bilic and the club have moved to have it reversed.
"The FA have been informed of our intention to appeal," a club spokesman told PA.
Feghouli, who was making his first Premier League start since joiningWest Ham from Spanish side Valencia on a free transfer last summer, is in danger of missing Friday's FA Cup match with Manchester City and league matches against strugglers Crystal Palace and Middlesbrough.
