Chantelle Firth was rushed to hospital after the accident at Pentland Primary School in Billingham, Teesside, but medics were unable to save her.
Police are investigating to determine how the incident occurred.
A Cleveland Police spokeswoman said officers were called to the school at 1:05pm on Thursday.
She said: “Our thoughts are with the family and we have specialist officers supporting them.
“The girl appears to have died as a result of choking on a piece of food.”