Little Angels Nursery in Calne will remain closed at least until September 25 as police carry out an investigation.
Police arrested a 37-year-old woman on Saturday but have not said what she is under suspicion of.
Ofsted has suspended the nursery's registration which means for the period of suspension it is an offence for Little Angels, in Curzon Street, to provide childcare.
The Government education watchdog suspends a provider’s registration if they believe a child or children may be at risk of harm. After a six-week period the suspension will be reviewed and possibly extended.
A spokesman for Wiltshire Police said: “We can confirm that police are conducting an investigation into allegations relating to Little Angels Nursery in Calne.
"The nursery has been closed by Ofsted and staff from the nursery are in the process of informing all parents of the closure.
“We can confirm that one woman, aged 37, was arrested on Saturday, August 16, and was taken to Melksham Police Station.
"She has since been released on police bail. Enquires continue.
"We are in the early stages of an investigation and it would be inappropriate to comment further on this matter.”
Rachel Cartmell, owner and a director of Little Angels, released a statement saying that she had not been arrested but was unable to make any comment at this time.
She said: "My staff and I are fully co-operating with the police and other agencies involved in the investigation."
A tweet from mother Danniloo Venes on Monday reads: “Shocked to hear the news about little angels in Calne! Glad my boys don't go 2 nursery now. A scary thing 4 any parent 2 hear!”
The nursery received a good rating when it was inspected by Ofsted on May 27 this year.
At the time of the inspection the nursery had 78 children on its roll ranging in age from less than one year old to eight. Its website said it was full for September 2014.
The Ofsted report said: “Children make good progress in the areas of learning and development.
"Staff have a strong knowledge and awareness of the provider’s policies and procedures for safeguarding which they implement effectively to protect children’s welfare.”
Police said they were working closely with the local authority and advised any parents with concerns to either call either Social Services emergency duty service on 0845 607 0888 or, during 8.45am to 5.20pm Monday to Friday, to call the Multi-Agency Safeguarding Hub (MASH) on 0300 4560108.
Anyone wanting to report a crime or who has information that might assist police can also call 101 or Crimestoppers on 0800 555 111.