The artwork on Churchfields depicts the 300 Barnsley men killed on the first day of the Battle of the Somme, July 1 1916.
It was created and unveiled at the town hall to mark the centenary in 2016 and later moved to the Peace Gardens at Churchfields.
On Saturday, Matthew Dunford was astonished to find that one of the panels had been broken. It is not known whether it was deliberate or accidental.
Matthew, 34, of Kier Street, said: “I am disgusted and disappointed that the memorial has been broken. It is there as a mark of respect for the people who died trying to protect us.
“If someone has taken the missing piece, it needs to be returned.”
Doreen Cureton, 70, who looks after the garden, spent Saturday afternoon trying to recover the missing piece. Doreen, of Victoria Crescent, said: “Me and my husband went round the garden with a leaf blower trying to uncover the missing panel.
“I even had a look through the bins to try and find it. I just find it disrespectful and upsetting.”
“The garden is a place where people can come and reflect and pay their respects and I’m upset that someone could do this.”
A council spokesperson said they have contacted the artists for a replacement panel and will arrange for it to be repaired.