West Midlands Police say he had been employed as an assistant at the Little Stars Nursery in Nechells for 18 months.
They believe only one child is involved and say the family has been informed.
Officers had a warrant to search the man’s house in connection with a different matter and then found evidence regarding a youngster at Little Stars.
Several items have been seized from the arrested man’s home, including a computer, telephones and various other electrical items.
Superintendent Matt Ward said: “When the computer was forensically examined, (it) led us to believe a series of serious sexual offences against a child had taken place at the Little Stars Nursery.
Little Stars opened in 2006 as part of the Nechells Regeneration Project
“The investigation is in its early stages but at the moment all our evidence suggests there is one offender and one child at the nursery.”
Supt Ward declined to comment on the initial allegations which led officers to arrest the man, adding: “That investigation is itself in its early days and it would not be appropriate to comment on that.”
Parents of children at the nursery spoke of their shock at the arrest, some claiming not to have known the school had been closed as a precaution.
One said: “I thought it was open – nobody called me.”
Another added: “Nobody has contacted me, nobody has told me anything. I study here and I am afraid for my kids really.”
Police said they would be contacting parents and guardians “at the earliest opportunity”.
Police say the nursery has been closed ‘as a precaution’
The latest Ofsted report reveals an unannounced visit was made by inspectors to Little Stars in August following a complaint.
As a result, the report says, it was concluded that the nursery “does not have an effective safeguarding children’s procedure”.
Speaking outside the nursery, Sky News’ David Crabtree said: “It was told to get that procedure in place – and it was, I understand, due for another investigation by Ofsted within the next few weeks.”
According to Ofsted, the nursery employs 14 members of staff and provides care for 55 children under the age of eight.
One website – findmyschool.co.uk – says it opened in 2006 and has two playrooms, one for babies and toddlers and the other for pre-school children.
“The nursery provides child care places for parents who are on training courses organised by the (Nechells Regeneration) Project,” the website adds.
A telephone number - – 0121 6754806 – has been set up for worried parents to offer advice and support.