Police said an Assistant Sub-Inspector (ASI), a head constable and four constables have been suspended for ill-treating the victim's parents when they went to lodge a complaint.
According to the police, the minor, a resident of Mandwa Basti in Kamla Nagar Police Station area, left her home on Saturday evening to fetch some grocery. When she did not return till late night, her parents, who work as labourers, reached the police to lodge a report but they refused.
The police got active only after receiving a call from the area's corporator around 11 p.m. The girl's body was recovered from a drain on Sunday morning. The post-mortem report revealed the child was strangled to death after the rape.
Public Relations Minister P.C. Sharma who visited the hospital after the incident admitted the child's life could have been saved had the police acted promptly.
Additional Superintendent of Police, Akhil Patel said the police personnel have been suspended for not taking immediate action on the complaint.
State Home Minister Bala Bachchan said a suspect who lived near the victim's house has been identified. But since he was absconding, his family members have been detained. All out efforts are being made to arrest him.
This is the second such incident in Madhya Pradesh in two days. Another minor girl was raped and killed in Ujjain on Friday. The accused was arrested on Saturday.
Newly-elected MP Pragya Thakur visited the victim's family and expressed grief over the tragedy. She also demanded strict action against the accused.
Chief Minister Kamal Nath has assured quick action and all help to the family.
( With inputs from IANS )