The incident occurred at Soladevanahalli in Bengaluru on Wednesday.
The toddler was the third son of Basavraj, a migrant worker from Raichur, who sells snacks.
Police said the accused, a 14-year-old boy, whose parents hailed from Bagalkote, reared some pigeons at home.
The bird droppings had led to quarrel between his parents and neighbours including Basavaraj's family.
A couple of days ago, there was an altercation between both the families.
On Wednesday afternoon, the boy found one of the pigeons missing at home and spotted it sitting nearby on the road.
As he ran to catch the bird, the child reportedly came in between. By the time he could react, the bird flew away.
Police said the angry teenager allegedly took the child to a nearby plantation, dumped him on the ground and stamped him to death with his feet.
Later, he fled from the spot.
The toddler's parents went in search when they did not find him for quite sometime.
They found the child lying in the plantation and rushed him to a nearby hospital where doctors declared him brought dead, police said.
The police, who registered a case of murder, learnt from some neighbours that the child was last seen with the teenager.
A police officer said, "The initial probe reveals that pigeon was the cause behind the incident but we are investigating other aspects too."