The party's demand came after the minister's daughter was accused of using a girl to impersonate her during a medical entrance exam.
“The party minister has been asked to resign", Congress General Secretary Prithviraj Chavan told a news agency.
A private TV news channel had earlier reported that two youngsters, including a girl, were appearing in the examination for the kin of two politicians, namely GM Saroori and former Minister Ram Pal of the National Conference.
Rejecting the allegations against his daughter, Mr Saroori dubbed the whole row a “misinformation campaign" launched by vested interests.
Police is currently verifying the minister's claim that his daughter was pursuing her bachelor"s degree in the Government Women"s College.