The little girl is thought to have used a 5ft metal slide and then become stuck on the ropes that were part of another piece of equipment.
North Yorkshire Police have appealed for witnesses but said they did not believe there were any suspicious circumstances.
A spokesman said: "At this stage, police do not believe there are any suspicious circumstances and it appears that the girl has become entangled in a piece of play equipment.
"The police are carrying out an investigation into the incident to establish exactly what happened and would like anyone who was in the area at the time to contact them."
The youngster was pronounced dead in hospital after the accident in the play area - described as 'superb' by Ofsted - at York College Nursery, York, yesterday afternoon.
The £42-a-day nursery cares for the children of students at the college and provides work placements for students
In a statement the college said: "York College is absolutely devastated at the news of the very sad death of a child, following a tragic incident at the York College Nursery.
"Our thoughts are with the child's family and the children, families and staff at York College Nursery.
"Currently, York College staff are helping the emergency services with their enquiries and the nursery is closed today. Parents have been informed and will be kept updated with any further developments."
A spokesperson for the City of York Council said: "All relevant agencies are aware and will be working together over the next few days.
"Our thoughts are with the family of the child and staff at the nursery."
The girl was attending York College's nursery, which offers day-care for 112 children aged six weeks to five years.
As well as caring for children of the college's students, aged between 16 and 19, it also provides work placements.
Ofsted inspectors said the nursery was 'good' in its September 2009 inspection and praised the play area.
"Children use the superb outdoor facilities with gusto, as they have ample opportunities to be active and improve their skills of co-ordination, control, manipulation and movement," the report said.
"They thoroughly enjoy, digging, climbing, balancing, crawling, building and observing the world around them."
The nursery's website states that students on work placements are never left unsupervised with children.
More:Advice And Health
Suggested For You
Get top stories and blog posts emailed to me each day. Newsletters may offer personalized content or advertisements. Learn more