"Arjun Rathore (19) took the victim to a corner in the Treasure Island mall on Mahatma Gandhi Road, when she was playing in the gaming zone, and raped her," Deputy Inspector General (DIG), Indore, Harinarayanchari Mishra said, adding that the accused was arrested.
The victim had gone to the mall with her family members, the officer said, adding that after the alleged incident, she narrated her ordeal to her mother.
The people in the mall caught hold of Rathore and thrashed him, before handing him over to the police, the DIG said.
"We are reviewing the security arrangements in the malls and if needed, it will be strengthened further," the officer said.
Meanwhile, the Congress attacked the BJP government in the state over the issue.
"The incident took place in a crowded place like a shopping mall. It indicates that under the BJP rule, women are not safe and criminals are not scared of law," Madhya Pradesh Congress spokesperson Narendra Saluja said.