The arrested youths were identified as Shariq Alam (18), Saif Ali (20), Anil Dabar (20) and Sachin Maheshwari (23), Aerodrome Police Station In-charge K L Dangi said.
All the four accused have been charged under section 363 (abduction) and 376 (rape) of the Indian Penal Code (IPC).
According to police, the minor girl had gone missing on October 16 and since then her mobile phone was switched-off.
The father of the victim had approached the police and told them that he suspected Shariq Alam of having kidnapped his minor daughter.
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Alam told the police that he and the victim were studying in the same school.
"On October 16, Alam had asked the girl to come to a place here stating that he wanted to return some objectionable photos and videos to her. However, when she arrived, he forced her to get inside a car along with his friend and took her to Ujjain. To make her unconscious, she was given a sedative following which both of them, along with two others raped her," Dangi said.