The T-shirt incorporates a Mickey Mouse head into the sleeve of the post-punk band's 1979 debut album Unknown Pleasures.
The cover itself was adapted by Peter Saville from a visual representation in the Cambridge Encyclopaedia of Astronomy of the first pulsar discovered.
"Inspired by the iconic sleeve of Joy Division's Unknown Pleasures album, this Waves Mickey Mouse Tee incorporates Mickey's image within the graphic of the pulse of a star," the Disney Store website said.
"That's appropriate given few stars have made bigger waves than Mickey!"
Bassist Hook told NME: "From a legal point of view, the image is in the public domain, as Disney know and, in a funny way, it's quite a compliment for a huge conglomerate like Disney to pick up on a poor little Manchester band that only existed for a couple of years. It's quite startling.
"I'm amazed they're that hard-up that they need to prey on little indie bands, but I get the feeling that someone may have done it as a tongue-in-cheek compliment."
He added: "I spend a lot of my time policing Joy Division bootlegs and normally we ask for a contribution to be made to Ian's charity for Epilesy. So, maybe if we wanted to make Disney feel guilty we could suggest that they did that."
However, talking about the $24.99 T-shirt to the Manchester Evening News drummer, Morris said: "I was quite angry when I first saw it. No-one asked us. They're trading off the band and our album cover, but get away with it by apparently saying the design was 'inspired' by us.
"I don't like the design at all. It's horrible. I can't imagine any Joy Division fans wearing it. Or anyone for that matter. Clearly, no-one investigated the history of the band before coming up with this idea. It's bizarre."
Joy Division ceased when frontman Ian Curtis hanged himself in May 1980, two months before the release of their second album Closer.
Hook has been touring Joy Division songs with his band The Light in recent years.
Morris has rejoined the reformed New Order, which does not include Hook.
> New Order will never reunite with Peter Hook, says Bernard Sumner
> New Order's Peter Hook: 'I don't want to f**k band over'
Watch Joy Division performing 'Transmission' below: