The Austrian club said Molotov cocktails were among the weapons used to attack their fans as they arrived at the stadium for the match in Salonica.
Several videos have shown fans hurling a variety of firecrackers and other missiles at each other and at one point dozens of masked fans ran onto the pitch.
Despite the trouble, the match went ahead but started five minutes later than planned. PAOK won the first leg 2-1.
"Some supporters of the host club welcomed the Rapid supporters (and officials and players) with almost unimaginable hatred," Rapid said in a statement.
Rapid added that their supporters were attacked in the city centre before the game but the real trouble started when 14 busloads of their fans arrived at the stadium.
"Bricks, pyrotechnic objects and benches were thrown and even two Molotov cocktails, which detonated a few metres from the bus and blew a crater in the asphalt," they said, adding that stones were also thrown and police used teargas.
"It is probably due to only a huge amount of luck that in this situation no major injuries were caused."
Rapid acknowledged that their own fans later fired missiles at the PAOK sector in the stadium and accepted that the club were likely to be penalised.
European governing body UEFA would not comment on the incidents. PAOK were not immediately available to comment.