The Asylum maze has been part of Thorpe Park's annual Fright Nights for more than eight years.
Campaigners claim having actors chasing people around an asylum stigmatises mental illness.
Thorpe Park said the attraction was not offensive or a realistic portrayal of a mental health institution.
A petition organised by Katie Sutton, a mental health nursing student at the University of Salford, has attracted more than 900 signatures.
Miss Sutton said she first became aware of the maze through Twitter.
"Thorpe Park kept repeating to people that there weren't sufficient complaints.  I thought if we can get actual forms of people bothered about it, then it might help."
She said the matter had been discussed in one of her university classes and "everyone in the room was absolutely horrified".
The charity Rethink Mental Illness has carried out a poll on Twitter to gauge people's views.
Paul Jenkins, its chief executive officer, said: "While some people clearly feel very strongly about this, opinion has been mixed.
"While of course there's nothing wrong with a bit of Halloween fun, explicit references to 'patients' crosses a line and reinforces damaging stereotypes about mental illness."
In September, supermarket chains Tesco and Asda withdrew two Halloween outfits after they were criticised for stigmatising people with mental health issues.
Asda dropped its "mental patient fancy dress costume", and Tesco later withdrew its "psycho ward" outfit.
In a statement, a Thorpe Park spokeswoman said the negative comments were not "universally representative".
"This is primarily a matter of context. The maze is not something you happen upon when out shopping," she said.
"This maze is also in its eighth year of operation and is an obviously extreme and simulated experience which draws on classic horror film content.
"It is not intended, nor is it deemed to be by those who have actually experienced it, to be in any way offensive or to be a realistic portrayal of a mental health or indeed any other institution."
Calls to shut down a theme park Halloween attraction have been made in a petition whose organisers say it stigmatises mental illness.