Informed sources said the violence broke out in Ater segment between supporters of the ruling Bharatiya Janata Party and opposition Congress, during which several vehicles were damaged.
An election official said the violence was reported away from polling stations.
The Voter Verified Paper Audit Trail is being used in the two bypolls, apart from the electronic voting machines.
State Chief Electoral Officer Salina Singh said no reports of booth capturing were received.
In Ater, Arvind Singh Bhadoria (BJP), Hemant Katare (Congress) and Samajwadi Party's Dinesh Singh are in the fray.
In Bandhavgarh, Congress rcandidate Savitri Singh is pitted against Shivnarayan Singh of the BJP.
The counting of votes will be taken up on April 13.