The Premier League's basement club take on 13th-placed Newcastle United on Saturday.
Fer was sent off by referee Anthony Taylor in Saturday's third-round FA Cup 0-0 draw for a cynical trip on Wolverhampton Wanderers' Helder Costa.
Swansea manager Carlos Carvalhal said after the game that the foul was a "classic yellow card".
The club have now confirmed they have taken up the matter with the Football Association.
A statement on the club's website said: "Swansea City have lodged an appeal against Leroy Fer's sending-off at Wolves on Saturday.
"The midfielder was shown a straight red card in the 67th minute of the Emirates FA Cup tie for a foul on Helder Costa which was deemed by referee Anthony Taylor to constitute violent conduct."
Fer will miss Premier League games against Newcastle and Liverpool, as well as the cup replay against Wolves, if Swansea's appeal proves unsuccessful.