Four human rights organisations -- BLAST, BRAC HRLS, Manusher Jonno Foundation and Naripokkho -- filed the writ petition on Sunday.
It was filed with the bench of Justice Md Mozibur Rahman Miah and Justice Mohi Uddin Shamim.
The writ petition said the current penal code of rape is discriminatory in terms of gender equality.
It also sought amendment to Section 375 and 376 of Women and Children Repression Prevention Act 9(1).
Section 375, classifies “sexual intercourse by a man with his own wife, the wife not being under thirteen years of age, is not rape” as an exception.
Ekattor TV Senior Newsroom Editor Wahida Afsana earlier sent a legal notice to the authorities, including the secretary to the law ministry, seeking recognition of rape of a wife by the husband as a criminal offence.