The print was taken from Highgate Primary School, in Sileby, where it had been on the wall of head teacher David Godfrey's office.
The theft was discovered at 8am on Tuesday, but the school thinks it may have been removed during the school fete on Saturday, June 20.
A school spokeswoman said: "It may well have happened during the fete when we had visitors in the school.
"People were welcomed in but unfortunately it looks like someone left with the painting."
The value of the picture, of a leopard walking away from barcode which is made to look like a cage, has not been disclosed.
Police want to speak to anyone seen in the Heathcote Drive area carrying a black framed painting measuring about two feet by two-and-a-half feet.
Pc Richard Spivey, who is investigating the incident, said: "We would like to speak to members of the public who saw anyone acting suspiciously at the time.
"We would also like to hear from anyone in the second-hand arts industry who has been offered a painting like this, or anyone who knows someone who has recently acquired a piece of artwork."
Call police on 0116 222 2222 or Crimestoppers on 0800 555 111.