However, votes in the landslide-hit Kinnaur district, part of the constituency, will be polled June 27. The vote count will be held simultaneously June 30.
Electors could be seen reaching polling stations even before voting started at 8 a.m.
"There has been no report of any delay in starting the poll process," state Chief Electoral Officer Narinder Chauhan told IANS.
A total of 11,24,786 voters will decide the fate of four candidates, including two independents. The main contest is between the ruling Congress and the opposition Bharatiya Janata Party (BJP).
The Congress has pitted Pratibha Singh, former MP and wife of six-time Chief Minister Virbhadra Singh, against BJP's former minister and sitting legislator Jai Ram Thakur.
The by-poll was necessitated after Virbhadra Singh was elected to the state assembly in December 2012.
The chief minister and his family will cast vote in Rampur, some 120 km from the state capital Shimla.
The Mandi constituency, which includes Kullu, Mandi and some areas of Chamba and Shimla districts, besides the tribal-dominated assembly constituencies of Kinnaur and Lahaul and Spiti, is one of the biggest in the country.