The Central Bureau of Investigation (CBI) has also registered FIR against 20 other unknown persons.
The FIR against all of them has been filed under various sections of the Indian Penal Code including murder, attempt to murder, criminal intimidation and criminal conspiracy.
The MLA's brother is Manoj Singh Sengar.
Others accused in the FIR are Vinod Misra, Hari Pal Singh, Navin Singh, Komal Singh, Arun Singh, Gyanendra Singh and Rinku Singh and advocate Awadhesh Singh. They are all residents of Unnao, where the rape victim hailed from.
Accused Arun Singh is the son-in-law of another Minister of State in Uttar Pradesh, Ranvendra Pratap Singh aka Dhunni Bhaiyya.
He is the Minister of State for Agriculture, Agriculture Education and Research in the Yogi Adityanath government and a BJP MLA from Husainganj in Fatehpur. Arun Singh, close to Kuldeep Sengar, is a block pramukh from Nawabganj in Unnao.
Ram Singh, CBI's Additional Superintendent of Police in Lucknow, has been asked to carry out the investigation.
The CBI move comes after the Centre on Tuesday handed over the probe into the truck-car collision to the CBI. The accident has also left the rape victim's lawyer battling for life.
On Sunday, the rape victim, who had accused Kuldeep Sengar of raping her in 2017, was travelling to Rae Bareli with her lawyer and two relatives when a truck being driven on the wrong side hit them.
One of the dead woman was a witness to the crime.
The truck that crashed into the car in Rae Bareli belonged to a Samajwadi Party leader from Fatehpur.
The CBI team has already collected the relevant case documents and other details from the Uttar Pradesh Police and will start investigations by visiting the crime scene.
An order from the Department of Personnel and Training said the case was being handed over to the agency to probe "abetment and conspiracies" in the accident.
Kuldeep Sengar has been in jail since a FIR was filed against him.
( With inputs from IANS )