The argue that a milk bank creates the risk of marriage between people who have drunk the milk of the same woman, which they say is forbidden by the religion, the bdnews24 report said on Sunday.
The government's Institute of Child and Mother Health (ICMH) was scheduled to launch the milk bank, fitted with imported machinery, on December 1.
But when the plan was made public, a group of Olamas, or Islamic scholars, opposed it.
They sent a legal notice claiming that the milk bank will create legal and religious complications.
The ICMH then stopped going ahead with the project.
"We've paused the project for now," said Project Coordinator Mojibur Rahman.
He decided to go ahead with the projest after discovering that Muslim-majority countries like Iraq, Iran, Pakistan, Kuwait and Malaysia also have human milk banks.
Gazi Ataur Rahman, a joint secretary general of the Islami Andolan Bangladesh and secretary general of National Olama Mashayekh Aimma Council, thinks the ICMH should have consulted the Islamic scholars before initiating the project as it is a "sensitive" issue.
"Marriage with 14 relations is 'haram' (forbidden in Islam). This applies for the relations created by drinking milk. It cannot be taken so lightly," bdnews24 quoted Rahman as saying.
The scholars will stick to their opposition to the project until issues like how much care will be taken in the process to preserve and distribute the milk becomes transparent to them, according to Ataur.
Meanwhile, a staffer at Dhaka Shishu (Children) Hospital's neonatal department, thinks a human milk bank was essential for vulnerable children.
He said the infants remain at NICUs away from their mothers most of the time.
"A milk bank can be useful for such babies," he added.
( With inputs from IANS )