The West Ham star was filmed kicking, slapping and hurling a pair of shoes at the pet as it tried to run away.
UFC's Blachowicz - most known for his impressive win over superstar Israel Adesanya in 2020 - has sent out a message to the 27-year-old.
"If you are so tough motherfu**er, Kurt Zouma, try to kick me," wrote Blachowicz. "What a piece of shit. No tolerance for animal cruelty."
Petition continues to increase
Over 120,000 people have signed a petition for Zouma to be prosecuted and Essex Police are currently investigating the issue.
A petition on Change.org, started by Anti Animal Abuse, reads: "In the UK we have laws against the abuse of animals, laws which should be applicable to everyone rich or poor, famous or not!
"We ask that the Metropolitan Police and RSPCA carry out an urgent investigation and prosecute the perpetrators of this heinous act.
"Further we ask that the RSPCA remove all animals from Zouma's 'care' immediately!
"Failure to take action in this case will send the message that animal abuse for entertainment is justified, that for the rich and famous breaking the law is no problem! Neither are acceptable!"
Experience Kissimmee, West Ham's official destination partner, has said it "will be evaluating our relationship and sponsorship with the club" after Zouma was selected for Tuesday's match.
A post by Experience Kissimmee on Twitter said: "It was disheartening to learn that the player Kurt Zouma was part of the starting line in West Ham United's game. As we wait for further information from WHU, we will be evaluating our relationship and sponsorship with the club."
What has David Moyes said?
Despite being an 'animal lover', David Moyes was quick to remind listeners of what he was employed to do - to select his best team and win football matches.
"Oh, 100%," Moyes said when asked if he was upset with Zouma.
He told BBC Match of the Day: "It's something we're all disappointed with and something we can't understand.
"He'll learn from it [but] today I had to pick a football team that gave me the best chance of winning the game as manager of West Ham.
"I know how people feel, but I'm also a football manager here.
"My feeling was that Kurt has apologised and I understand a lot of people will not just be accepting of an apology. But to me, he came out and [apologised] honestly and I had to do my job.
"I have spoken to [Zouma] and we will move on as much as we can," Moyes added.
Kurt Zouma's statement
While West Ham "unreservedly condemned" Zouma's conduct, the player himself assured his two cats are 'fine and healthy'.
"There are no excuses for my behaviour, which I sincerely regret.
"I also want to say how deeply sorry I am to anyone who was upset by the video. I would like to assure everyone that our two cats are perfectly fine and healthy.
"They are loved and cherished by our entire family, and this behaviour was an isolated incident that will not happen again."