The Eagles released a statement on Thursday (AEST) threatening legal action against the perpetrators and calling for co-operation from other Premier League clubs.
"Crystal Palace Football Club has taken action after one of our players, Wilfried Zaha, has again been subjected to racist abuse on social media," the statement said.
"We will not tolerate this behaviour being directed at any of our players and will fully support them in dealing with such incidents.
"Any action we can take unilaterally as a club will be taken immediately and we will also seek cooperation from other clubs where relevant, following that we will pursue the matter criminally with the full force of whatever the law allows."
Cote d'Ivoire international Zaha previously said he received racist abuse and death threats on social media after winning a penalty in a 2-2 Premier League draw with Arsenal last October.
In an Instagram post at the time, he said: "For all the people taking it one step further and being racist and wishing death on my family, I wish you and your families the best too.
"My life is still very good despite your hate."