Sengar was picked up from his home around 4:30 and is being questioned by the CBI, an official told News18.
The investigating agency also registered three separate cases late on Thursday after the case was taken up by the CBI following a notification by the Personnel Ministry, news agency PTI stated.
The decision to hand over the twin cases, of the alleged rape of the woman and the custodial death of her father, was taken after the Special Investigation Team constituted under Additional Director General of Police (Lucknow zone) to look into the matter submitted its report to the government.
The MLA was booked under relevant sections of the Indian Penal Code and POCSO at Unnao’s Makhi Police Station on Thursday morning, hours after he made a dramatic appearance before the police but refused to surrender.
The matter came to light after the woman attempted suicide outside the residence of Chief Minister Yogi Adityanath on Sunday, triggering a massive row over women's safety in Uttar Pradesh.
Later, the state police had arrested her father who died in judicial custody with autopsy suggesting several injuries on his body.
A relative of Sengar was quoted by news agency ANI claiming that the family itself demanded a CBI inquiry in the matter.
Unnao Rape Case: We ourselves had demanded a CBI inquiry. This morning CBI came & asked us to come to the CBI headquarters as they wanted to talk: Prakhar Singh, relative of BJP MLA Kuldeep Singh Sengar pic.twitter.com/oxMBmXGXFu— ANI UP (@ANINewsUP) April 13, 2018
A day earlier, the Allahabad High Court came down heavily on the Uttar Pradesh government and asked whether it proposes to arrest accused BJP MLA Kuldeep Singh Sengar.
A bench of Chief Justice D B Bhosale and Justice Suneet Kumar, heard the matter in detail and will pronounce its order on Friday. The court also questioned the conduct of the police in the case, saying that the law and order situation seems to have collapsed in the state.