The theft happened sometime between Monday, March 7 and Sunday, March 13, when the owners discovered the garage door had been forced open and two go-karts had been taken from inside.
Also taken from the garage was a spare go-kart chassis and a trolley.
One of the go-karts, a Birel Rotax, has a red chassis, a white and black seat with a small crack in it and distinctive digital control on the steering wheel.
Police are urging anyone with information about the theft to call them immediately.
PC Lucy Johnson, the investigating officer, said: “The family are extremely upset. The children built the go-karts themselves so they hold a lot of sentimental value.
“I would like to urge anyone who has information about the current whereabouts of the go-karts to come forward and help us return them to their owners.
“If you know where the go-karts are, know who was responsible for taking them or even witnessed the theft then please get in touch, it isn’t too late to help us with our enquires.”
Anyone with any information is asked to contact PC 4724 Lucy Johnson on Leicester (0116) 222 2222, follow the instructions to leave a message for a police officer and when prompted key in the officer’s identification number 4724. Alternatively, contact Crimestoppers, which is free* and anonymous, on 0800 555 111.