Two of his associates, Ashok Tiwari and Ashish Shukla, have also been convicted.
Judge Pawan Kumar Rai of a special MP/MLA court in Lucknow held Prajapati guilty of gang rape charges in the case under Sections 482/378/407 of the Indian Penal Code.
The quantum of punishment will be announced on Friday.
In this case, seven people, including Prajapati, were charged.
A woman from Chitrakoot had accused former Samajwadi Party Minister and his friends of gang rape. The woman also alleged that the accused forcibly had physical intercourse with her minor daughter.
On the directions of the Supreme Court, an FIR was lodged against Prajapati and six other accused on February 18, 2017. All of them were charged with gang rape, threat to life, and violating the POCSO Act.
Apart from Prajapati, Vikas Verma, Amarendra Singh, Chandrapal, Rupeshwar, Shukla, and Tiwari were also charged in this case.
Prajapati and the other accused were arrested and imprisoned after the FIR was filed.