Up to 28,000 are expected at Alton Towers on September 17 when there will be no music, booze or gambling.
Instead there will be prayer areas, Muslim stalls and all food served will be HALAL.
Organisers Islamic Leisure have billed it the First National Muslim Fun Day and tickets can only be bought through their website.
Non-Muslims phoning the Staffordshire park have been refused tickets.
One, George Hughes, 19, who rang up for 15 tickets for a pal’s birthday, said: “I couldn’t believe it.
Invited ... Muslim girls can go to the fun day
“It’s the only day we can go, yet I can’t because I’m not Muslim. Can you imagine all the fuss if there was a Christians-only day?”
George, of Crayford, Kent, added: “My Muslim friends think it’s outrageous.
“What’s the world coming to when people are being banned from flying the St George’s flag yet this sort of day is allowed? If it must be held, then why not on a weekday rather than a busy weekend?”
The event is widely promoted on the internet and the Muslim Public Affairs Committee declared it “exclusively for our brothers and sisters”.
Logo ... biggest fun park
But some Muslims have condemned the idea. One university student on a Muslim website forum said: “It’s hardly encouraging integration.”
Another said: “What next . . . an all Muslims shopping day out in the Trafford Centre in Manchester?”
Abid Hussan of Islamic Leisure insisted the day was open to all faiths, although Islamic laws would apply.
He added: “There will be no smoking, no alcohol and halal food only.
“We’re trying to get Muslims to go to this day because they wouldn’t normally go somewhere like Alton Towers. We’re trying to integrate Muslims into the wider community. People can come down and see the way we live. It will be a peaceful family environment.”
Alton Towers said any organisation could hire the park for a day.
A spokeswoman said “We make no distinction regarding sexuality, religious, ethnic or lifestyle choices.”
She confirmed tickets for the day were now available only through Islamic Leisure. And Alton Towers would promote the fact that the day had been booked.
She added: “As a general rule, there will be no admission on the day to guests who have not booked through the organisation in advance.”