Police believe the woman, aged in her 20s, walked onto the tracks of the ride to retrieve her phone on Sunday evening.

She was hit by a carriage around 5.45pm and fell injured to the ground.

The woman was taken to Royal Melbourne Hospital with critical injuries to her face.

The hospital said on Monday morning her condition was unchanged.

Police and Worksafe are investigating the incident.

All of the rides at the show had been cleared by Worksafe before they began operating last Thursday, Melbourne Royal chief executive Brad Jenkins said.

The operator of the roller-coaster involved in Sunday's incident was "absolutely devastated", Mr Jenkins said.

"'It's a very tight knit show community ... and everyone is totally devastated," he told ABC Radio Melbourne on Monday morning.

"The show is about putting smiles on people's faces and tragedies like this are just devastating for everyone involved."

Melbourne Royal Show will remain open this week as investigations continue and Mr Jenkins is hopeful patrons will not be deterred from attending.

"It was a tragic accident," he said.

"It had nothing to do with a ride malfunction or anything of that nature.

"I'm confident all of the rides have been signed off by Worksafe and are safe."

Australian Associated Press