The Amsterdam club will host the Hoops in a Uefa Champions League clash in Holland.
But visiting fans won't enjoy the experience, according to Dutch League side Go Ahead Eagles.
The club's president has taken the unusual step of writing to Ajax to complain about the treatment their fans received on a visit to the Amsterdam Arena earlier this month.
Erwin Lugt said: "After the game, we were inundated with complains from our supporters about their reception at the Arena.
"Both our supporters and our stewards did not feel welcomed.
"The feeling was a hostile atmosphere from both the police and Ajax fans."
Ajax were hit this week with a £25,000 bill from Celtic for their destruction of seats at Parkhead.