Dutch captain Mark van Bommel branded the monkey chants as “a real disgrace”.
Van Bommel said: “You need to open your ears. If you did hear it, and don’t want to hear it, that is even worse.”
Uefa officials said an incident had occurred but it was a protest about Krakow not being given any Euro 2012 matches, The Times reported.
The news comes on the opening day of the tournament, which is being co-hosted by Poland and Ukraine.
“It’s the last thing Uefa needs – just a few hours before the opening game. The issue of racism has stalked the preparations for this competition and once again it has reared its head.”
A BBC documentary had recently raised fears that Euro 2012 could be dogged by the issue of racism.
The Dutch players were reportedly targeted by Polish fans as they began their practice session at the Stadion Miejski.
Van Bommel responded by leading the squad to the far side of the pitch.
The abuse comes just a day after they had visited Nazi German concentration camp Auschwitz, which is nearby.
Van Bommel said: “It is a real disgrace, especially after getting back from Auschwitz, that you are confronted with this.
“We will take it up with Uefa and if it happens at a match we will talk to the referee and ask him to take us off the field.”
“It became worse on the second lap, at which point Van Bommel took the players to the other side of the stadium. It’s the only story in the Dutch press today.” said the Dutch captain.
Earlier this week Uefa president Michel Platini told BBC Sport that referees have been instructed to call a halt to matches at this summer’s tournament if a player is racially taunted.
Yet the Frenchman also warned any player who left the field unilaterally in protest over abuse from the stands would be yellow carded.
Italy and Manchester City striker Mario Balotelli had earlier said he intended to do exactly that if he found himself being racially abused.
Former England centre-back Sol Campbell, meanwhile, was compelled to advise fans to avoid the tournament after seeing the Panorama footage of supporters in Ukraine giving Nazi salutes and taunting black players with monkey noises.
Meanwhile, the families of black England players Theo Walcott and Alex Oxlade-Chamberlain have declined to travel to watch the matches because of fears over racism.