Supreme Court lawyer Advocate Md Mahmudul Hasan filed the writ.
The article 41 of the Constitution guarantees every citizen the right to profess, practise or propagate any religion. But the Muslim women are facing discrimination, the writ said.
The centre point of practising Muslim religion is mosque.
It has given equal right for men and women to practise religion inside the mosque, the writ said.
The hearing on the writ is likely to be held with the HC bench led by Justice JBM Hassan in the next week, said Mahmudul Hasan.
The women in Bangladesh are facing discrimination although they have the equal right as per the Constitution.
Measures should be taken to arrange separate prayer space, ablution space and toilets for women at all mosques across the country, the writ petitioner said.