The company said it had opened an independent disciplinary investigation.
It did not give details of the allegations, but The Times newspaper reported that he has been accused of sexual misconduct with students.
The 33-year-old, who began as a dancer with the Royal Ballet, has not commented on the allegations.
Scarlett has been artist-in-residence at the company since 2012.
He has been responsible for creating some of their major recent shows, including a new production of Swan Lake in 2018, which is being revived this spring.
A spokesperson for the Royal Opera House, where the Royal Ballet is based, said: “We were made aware of allegations relating to Liam Scarlett in August 2019. The individual was immediately suspended, and an independent disciplinary investigation opened.
“The Royal Ballet Company has a code of conduct in place to ensure staff and visiting artists are always supported. As the process is still ongoing, and as a duty of care to staff and artists, we are unable to comment further until the matter has been concluded.”
He was appointed artistic associate at Queensland Ballet in 2016, but that company has now said it has “suspended all future engagements with Liam Scarlett pending the results of that investigation”.
Its statement added: “Queensland Ballet has a strong ethos surrounding wellbeing in the arts and is committed to the provision and maintenance of a healthy and safe environment for all.
“And there is a code of conduct in place to ensure the entire QB community are always supported in order to achieve this. As the investigation in the UK is ongoing, and as a duty of care to all involved, we are unable to comment further.”