The lockdown came into force at 6 pm on Friday.
Among these places, Ratlam, Betul, Katni, Khargone and Chhindwara districts, all bordering Maharashtra, have been seeing record spikes in infections over the past few days.
Ratlam and Betul will be under lockdown for nine days, while it will be from Friday till the morning of April 16 in Chhindwara, close to Nagpur, the biggest city in Maharashtra's Vidarbha region.
The lockdown will be in force for a period of seven days, which started on Friday night, in Khargone and Katni, officials said.
However, thanks to an Assembly bypoll scheduled on Apil 17, Damoh remained "open" for campaigning, officials pointed out.