Police are investigating after the headstone was kicked to pieces .
The cemetery - in Dogdyke Road - is owned by Coningsby Town Council.
Town clerk Kathy Roberts admitted no-one could understand why the headstone had been targeted.
She said: “It’s just one headstone in a section of the cemetery which is reserved for children.
“The parents no longer live in the village. I spoke to them and they are devastated.
“They can’t understand why someone would do this.
“It’s just so sad and you really feel for the family.”
Mrs Roberts said the damage was spotted last Friday. She explained that the family had visited the cemetery and had ‘cleared’ the damage
She added the headstone was ‘damaged beyond repair’.
Mrs Roberts said there were ‘footprints’ on a vandalised plinth.
She said it was the first instance of vandalism at the cemetery but admitted it is difficult to improve security as people need access.
The town council is to discuss paying for a replacement.
According to police, the damage took place between February 25 and March 10.
PCSO Nicola Stuchfield of the Neighbourhood Policing Team said: “The heart shaped stone has been kicked repeatedly until the plinth has smashed.
“If you have any information call 101 quoting incident number 161 of 19/03/16. Alternatively call Crime Stoppers anonymously on 0800 555 111.”