He has been sent to judicial custody for 14 days.
Mr Prajapati had been absconding for over two weeks; he went missing in the middle of campaigning for the UP assembly election after the Supreme Court ordered the state police to file a case against him on the allegation of a woman that the minister had, along with six other men, gang-raped her and attempted to rape her 16-year-old daughter in October.
Gayatri Prajapati, a senior Samajwadi Party leader, lost the assembly election from Amethi, the constituency he had won last time.
The Supreme Court order in the middle of the crucial UP elections had put outgoing Chief Minister Akhilesh Yadav of the Samajwadi Party on the backfoot, with the BJP accusing him of shielding his partyman. The party also attacked Mr Yadav for campaigning for Mr Prajapati - Akhilesh Yadav's first public rally had prominently featured the minister. Akhilesh Yadav and his party have denied protecting Gayatri Prajapati.
On Saturday, the BJP swept the UP elections winning 325 of the state's 403 seats along with its allies. Akhilesh Yadav's Samajwadi Party could win only 47 seats and his campaign is seen to have been severely impacted in the latter rounds of the elections by the Gayatri Prajapati controversy.
In his first speech after the election results, BJP chief Amit Shah had promised that Mr Prajapati would be traced and arrested soon.
The police said they suspect Mr Prajapati returned to Lucknow this morning. They said they had zeroed in on two possible places where the politician on the run could possibly have been hiding - a mining town in UP's Bundelkhand and another location in the eastern part of the state.
All the six other people named by the police in the case have already been arrested. They include two of the minister's close aides and a security guard. Three were arrested yesterday in Lucknow and the police had also brought Mr Prajapati's son, Anurag Prajapati, a businessman, from Amethi to Lucknow to question him.
The UP police had filed a First Information Report or FIR against Mr Prajapati and the six other people on February 17 on the orders of the Supreme Court. The court has sought an action taken report within eight weeks.
When a non-bailable warrant was issued for his arrest, Gayatri Prajapati absconded. His passport has been impounded and airports across the country were alerted about the possibility of his trying to flee the country.