The police action comes on a day when Prime Minister Narendra Modi accused alliance partners SP and Congress of chanting "Gayatri Prajapati Mantra".
Police said raids were also being conducted in Lucknow, Kanpur and Amethi to trace Mr Prajapati who is absconding after the 49-year-old SP leader was booked following a Supreme Court directive.
"Passport of rape accused minister Gayatri Prasad Prajapati has been impounded," ADG (Law and Order) Daljit Chaudhary told PTI.
He said UP police will approach the Ministry of External Affairs to get the passport cancelled.
Mr Chaudhary said Non-Bailable Warrants (NBW) had been issued against Prajapati and six others in connection with the case of alleged gangrape of a woman and attempt to rape her minor daughter.
He also said a look-out notice has been issued and raids were being conducted to trace Mr Prajapati.
Mr Chaudhary said that to ensure that Mr Pajapati is arrested soon, the Special Task Force of UP police has been roped in, especially to prevent him from crossing the country's borders.
The action also comes a day after airports across the country were alerted about the possibility of Mr Prajapati trying to flee the country.
Earlier in the day, at an election meeting in Jaunpur, PM Modi said, "In this country, when we do something good, we chant the Gayatri Mantra. But, the SP-Congress alliance is chanting the 'Gayatri Prajapati Mantra'.
"A daughter is seeking justice and the chief minister is shielding the gunehgaar (guilty)...What bigger blot can there be than this that in Uttar Pradesh when a buffalo goes missing, the government runs to find it.
"But, a girl is crying for justice and the police and chief minister are sleeping...Such a government needs to be punished," he said, reminding voters that they have got an opportunity to perform the "pind daan" (last rites) of their "tormentors".
Uttar Pradesh has a long porous border with Nepal and is manned by SSB, a border guarding force of the Union Home Ministry, which has also been alerted about the possiblity of such a move by Mr Prajapati.
Official sources said a Letter of Cancellation (LC) will soon be opened against Prajapati and all airports have been alerted to prevent the SP leader from fleeing the country.
A letter of cancellation is a technical term used for alerting immigration authorities about any possible move by a suspect to leave the country.
Whenever passport of the suspect comes for immigration clearance at any exit point of the country, the computer screen warns the official to not let the person leave.
The UP Police registered an FIR against Mr Prajapati, who continues to elude them, for allegedly gang-raping a woman and molesting her minor daughter with his aides.
The FIR was filed recently following a directive of the Supreme Court after the alleged victim woman approached it.