In the show, titled Panic On The Streets of Springfield, Lisa Simpson becomes obsessed with the militantly vegan singer of a 1980s indie band.
But her dreams are shattered when it transpires her idol, voiced by Benedict Cumberbatch, had become a bitter, overweight, anti-immigrant meat-eater.
A statement on Morrissey's Facebook called the show "hurtful and racist".
"Surprising what a 'turn for the worst' the writing for The Simpson's TV show has taken in recent years," said the statement, which was posted by the star's manager, Peter Katsis.
"Poking fun at subjects is one thing," it continued, "but when a show stoops so low to use harshly hateful tactics like showing the Morrissey character with his belly hanging out of his shirt (when he has never looked like that at any point in his career) makes you wonder who the real hurtful, racist group is here.
"Even worse - calling the Morrissey character out for being a racist, without pointing out any specific instances, offers nothing. It only serves to insult the artist."
The statement went on to accuse The Simpsons of hypocrisy, noting that white actor Hank Azaria had recently bowed to criticism and agreed to stop voicing the Indian character Apu Nahasapeemapetilon.
"Hank Azaria's recent apology to the whole country of India for his role in upholding 'structural racism' says it all," the message said.
Prior to the episode airing, Morrisey's official Facebook page had promoted the show by posting a still image from the animation.
The show said it would not be commenting on the star's latest statement.
'Hamburger Is Homicide'
However, the episode's writer previously insisted that the character was not solely based on Morrissey.
"I'm sticking by that," Tim Long told Variety magazine, adding: "The character is definitely Morrissey-esque, with maybe a small dash of Robert Smith from the Cure, Ian Curtis from Joy Division, and a bunch of other people".
Called Quilloughby, the character was said to be the lead singer of a band called The Snuffs - a stand-in for The Smiths.
The episode also featured music by Flight Of The Conchords and The Muppets' songwriter, Bret McKenzie; and included parodies of The Smiths song titles, such as How Late Is Then, Hamburger Is Homicide, and Everyone Is Horrid Except Me (And Possibly You).
Long said the episode had been inspired by his love of British indie bands during the 1980s, recalling how seeing The Smiths on their The Queen Is Dead tour had "changed my life".
"I've seen Moz [Morrissey] many times since then, most recently at the Hollywood Bowl in 2018," he explained to Variety.
"Executive producer Matt Selman was also at that show, and we got to talking about how much music meant to us as weird, alienated teenagers - and also how being a big fan of someone is like having a lifelong relationship with them, with all the ups and down that implies. This show grew out of that discussion."
In recent years, Morrissey has been criticised for his outspoken and controversial views.
He has called halal meat "evil", accused London Mayor Sadiq Khan of being unable to "talk properly" and appeared to defend actor Kevin Spacey over allegations of sexual abuse.
The singer has also expressed support for the far-right For Britain party, wearing a badge with its logo on during a US TV performance.
He has consistently denied being a racist.
Panic On The Streets Of Springfield has yet to be broadcast in the UK, but is expected to premiere on Sky One next month.