Police said the injuries on the girl's body suggested she was sexually abused. (FILE PHOTO)

A five-year-old girl whose body was found floating in a river in Madhya Pradesh's Ujjain yesterday was raped and murdered, police said on Saturday.

"The girl was raped and murdered. We have constituted a Special Investigation Team (SIT) to probe the case. We are interrogating the suspects," Sachin Atulkar, Ujjain's Superintendent of Police, told reporters.

The family members of the girl registered a complaint after she went missing on Friday. Police then found the body of the girl floating in river Shipra.

Police said the injuries on the girl's body suggested she was sexually abused.

Three people have been arrested in the matter, including the girl's uncle.

Meanwhile, the opposition in Madhya Pradesh has raised questions over the law and order situation in the Congress-ruled state after the incident.

BJP legislator and Leader of Opposition in the Madhya Pradesh assembly attacked Chief Minister Kamal Nath over the incident, blaming the shake up in the police department for a "spike" in crime in the state.

"This is an unfortunate incident. The rape and murder of a five-year-old girl in Ujjain raise questions on the state's law and order situation. There is no control over criminals. Officials should not be transferred in a quick manner as it encourages the criminals," Mr Bhargav told news agency ANI.