A woman and a minor boy were among those killed in the mishap which took place near a petrol station at Runija village, about 60km from the district headquarters, they said.
Initial investigation suggests the jeep driver lost control over the vehicle after its front right side tyre got punctured. Thereafter, the vehicle overturned, Bhat Pachlana police station sub-inspector Shanker Singh Mujalda said.
Four persons were killed and 37 others, including the driver, injured, six of them seriously, in the mishap, he said.
The seriously injured passengers were rushed to Indore, while the others were admitted to different hospitals in the district, Mujalda said.
Passengers travelling on rooftops or clinging on to the doors of overloaded jeeps is a common sight in rural areas of Madhya Pradesh.
Mujalda said the deceased were identified as Kanhaiya Lal (50) Shanti Bai (55), Shambhu (35) and Ankit (15) - all local residents.