The family of the boy who died are members of the Kiev-led Orthodox church but the city is predominantly of the Moscow Patriarchate branch.
The boy's father, Roman Polishchuk, said he asked the Moscow denomination to bury his son but they refused.
He told local newspaper Forpost: "The priest said our baby was unchristened and our church was a sham."
"My wife cried and threw herself before him on her knees, but this did not help."
The priest reported that Polishchuk punched him inside the church before the family and that the father forced to leave.
Molchanov said he had no choice because those were the rules of his faith.
The Ukrainian Church divided into Moscow and Kiev-led branches when the Soviet Union collapsed in 1991 but tension has returned somewhat since crises in recent years in Ukraine.
The 21 month old boy died as well as the 39-year old man who fell on him on New Year's Eve.
