Emergency services said she was taken to the Royal Berkshire Hospital by ambulance but could not be saved.
Thames Valley Police said they were informed of her death soon after 4.30pm.
A statement posted on the school's website on Thursday said: "We are deeply saddened to report that one of our children passed away today.
"Our thoughts are very much with the family and friends at this tragic time."
The website said that "after careful consideration" staff had decided to that the school would be closed on Friday.
The child has yet to be named. Details about when a post-mortem examination and coroner's inquest will take place have yet to be released.
A Thames Valley force spokeswoman said: "The death is unexplained but not believed to be suspicious."
Judith Ramsden, director of children's services at Wokingham Borough Council, told the Local Berkshire news website: "This is an extremely sad day and our thoughts and prayers are very much with family and friends of the little girl, all of the pupils, their families, and staff at the school.
"We are supporting the whole school community in every way we can, and our specialist team will be back with them on Monday.
"We sincerely ask that you give the school, and its families, both the space and the time they need to grieve and heal during the coming months."