LL Camps has operated at Merry Hill in Bushey, Hertfordshire, for the past four years, describing itself as the UK's only American-style summer camp.
A man aged 25, of Borehamwood, had been bailed until September, said police.
They said they would contact families directly should they discover that any children had been affected.
A spokesman for Ofsted said: "We can confirm we have suspended the registrations of these early years settings while investigations are carried out.
"It would be inappropriate to comment further while investigations are ongoing."
In a joint statement, Hertfordshire Police and Hertfordshire County Council said they were working with Ofsted and the "safety and welfare of children is the top priority".
Anyone with specific concerns about a child is asked to call Hertfordshire County Council on 0300 123 4043.
A statement from the LL Camps team was posted its Facebook page on Thursday. It said the camp had closed with "immediate effect" and it "cannot disclose any further information".
The privately-run LL Camps is based at St Margaret's School in Bushey.
A school spokeswoman said LL Camps was "entirely non-related to our school" and St Margaret's had "no links to LL Camps except to hire out a part of the Sports Centre site during the holiday periods".
The LL Camps website, which has been taken offline, stated it had achieved "outstanding early years provider" awards from Ofsted in 2013 and 2014.
It said the camp was about "meeting new friends, expanding interests and learning new skills". It added it was committed to its core values of creating a "caring, nurturing and positive" environment.
A children's summer camp has been closed by Ofsted after a man was arrested on suspicion of possessing indecent images of children.