The club condemned the song about Alvaro Morata by their fans during Saturday’s 2-1 win over Leicester City.
Chelsea head of communications Steve Atkins said offenders will be banned if there is sufficient evidence.
“People should know that the police will be involved. We must be clear on this because it has to stop,” he said.
“Chelsea Football Club finds all form of discrimination abhorrent. The language used in that song is totally unacceptable.
“People that use this kind of language against others always try and argue a grey area. There is no grey area. That language used was anti-Semitic. We have a zero tolerance towards it.”
The chant about Morata, who scored against Leicester, was used to abuse London rivals Tottenham, who have a large Jewish fanbase.
After the game, Morata tweeted: “Since I arrived, I have been able to feel your support every single day, you are amazing and I’d like to ask you to please respect everyone!”
Speaking before Chelsea’s Champions League game against Qarabag, manager Antonio Conte supported the statement from the club.
“You know very well that I love our fans because they push us a lot during the game,” he said.
“But I think we must pay great attention in the future.”
Kick It Out, football’s equality and inclusion organisation, has also condemned the song and called for those responsible to be banned.