A total of 22 candidates from Ashoknagar's Mungaoli and 13 from Kolaras in Shivpuri district are in the fray.
As many as 2,44,457 voters from Kolaras and 1,91,009 from Mungaoli will exercise their franchise between 8 a.m. and 5 p.m.
Some 3,000 poll officials are conducting the process at 575 polling stations, the Election Commission said.
The assembly seats fell vacant after the death of sitting Congress MLAs Mahendra Singh Kalukheda (Mungaoli) and Ram Singh Yadav (Kolaras).
These bypolls are being seen as a prestige battle for Shivraj Singh Chouhan, who is in his third term as Chief Minister, and his arch-rival Jyotiraditya Scindia of the Congress.
The two assembly segments are parts of Scindia's Guna Lok Sabha constituency.
The votes will be counted on February 28 and the results will be declared the same day, the EC said.
Electronic voting machines (EVMs) and voter verifiable paper audit trail (VVPAT) machines are being used at all polling booths.