The accused Sanjeev Joshi alias Nanda took the girl to a secluded place and raped her yesterday, Superintendent of Police (SP) Saumitra Yadav said.
He later dropped her home.
The incident came to light this morning when her family members took the girl to a doctor after she cried of pain last night, he said.
An FIR has been registered in this connection, the SP said, adding, the accused has been arrested.