Mr Barsky wrote: “I want everyone to know that Mathias Glass is not Jewish. The stereotype driven character he portrays is offensive and distasteful. It is the equivalent of black face.
“I can make fun of myself and my people, but someone from outside the community has no right.”
Mr Barsky said he had messaged Mr Glass about the persona, and knows other Jews in wrestling who have urged him to stop.
The reaction to his Facebook post was mixed, with some social media users expressing sympathy, while others pointed out that exaggerated characters are a staple of professional wrestling.
On Sunday Mr Glass tweeted: “I find myself pulling back on some of the stereotypical stuff … but to the chagrin of many many Jewish fans, friends, and fellow wrestlers. I’m constantly evolving, constantly learning, and always willing to listen to constructive criticism.”