The sanctions were imposed by UEFA's disciplinary committee following a riot involving both sets of supporters at the Europa League play-off first leg at Greek side PAOK Salonika on August 23.
Fans hurled firecrackers at each other and some supporters, many of them masked, invaded the pitch before the game that was won 2-1 by PAOK.
Rapid, who won the return 3-0 to qualify for the group stage, were charged by UEFA with "improper conduct of supporters - crowd disturbances and setting off and throwing of fireworks and missiles".
Their one-year ban is suspended for a probationary period of three years, meaning they will be automatically excluded from European competition if there is a repeat.
Rapid were fined 75,000 euros and have also appealed against that punishment, UEFA said on Monday.
UEFA added the appeal hearing would take place on September 14.
Rapid's next European home game is against Norway's Rosenborg Trondheim on September 20.
PAOK were also given a suspended one-year ban, ordered to play their next three European home games behind closed doors and fined 150,000 euros.
- PAOK Salonika