Twelve of the dead were children born prematurely and were less than a month old, while others were suffering from advanced stages of meningitis and encephalitis diseases.
The protesters in Sunday's standoff said neglect had led to the deaths of the children at the overcrowded hospital which has faced criticism in the past for lack of life-saving equipment such as oxygen cylinders, ventilators, incubators and inadequate medical staff.
"We want resignation of the government, we want answers," read placards carried by the slogan-shouting activists of the Congress party. West Bengal state, where the hospital is located, is run by a communist government.
A few protesters managed to break through a police cordon and entered the hospital building in Kolkata, formerly Calcutta, before they were removed.
The B C Roy Memorial Hospital is the only facility dealing with critical child illness in eastern India, drawing patients from around the region.
A local health official denied any neglect and said the number of infant deaths was not abnormal.
"The deaths are not alarming at all, considering the fact that 4-7 deaths in a day is a routine affair"
Jayshree Mitra, Local health official
"The deaths are not alarming at all, considering the fact that 4-7 deaths in a day is a routine affair," said Jayshree Mitra.
At least, 40-50 children are admitted to the hospital every day, she said.
The hospital has 400 child patients on any given day but only 250 beds, forcing authorities to keep two to three infants on one bed.
In 2002, 31 babies died there within two days, triggering protests.
India's healthcare infrastructure is regarded as inadequate and inefficient for a population of over 1.1 billion.
Thousands of people die each year of common diseases due to lack of immunisation and an unclean environment.