Senior Superintendent of Police, Lucknow, Manzil Saini told PTI that Prajapati was arrested from Aashiyana area of the city early this morning.
He is likely to be produced before the POCSO Court later in the day, Saini said.
Six persons named in the FIR against the 49-year-old SP leader have already been been picked up by the police.
Police had yesterday interrogated the SP leader's two sons and nephew to get some inputs regarding his whereabouts.
Prajapati was booked on a Supreme Court directive and an FIR was lodged on February 17 against the minister and six others for allegedly gang-raping a woman and alleged attempt to rape her minor daughter.
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A Look Out notice was also issued against him as also a Non-Bailable Warrant. His passport too has been impounded.
Airports across the country had been alerted about the possibility of Prajapati trying to flee the country.
Reacting to the arrest of the SP leader, BJP leader Vijay
Bahadur Pathak said the "State police was till now politicised. As soon as it has been freed from political pressures it has started performing resulting in the arrest".