According to Election Commission officials, the polling was progressing peacefully and 31.34 per cent voters exercised their franchise by 11 a.m.
Polling began at 7 a.m. and will continue till 5 p.m. in 302 polling stations in the constituency in Suryapet district.
A total of 2,36,842 voters are eligible to exercise their franchise in the bypoll, the first since Telangana Rashtra Samithi (TRS) retained power in the state in December 2018.
There are 28 candidates, including three women, in the fray. The main contest is between TRS candidate S. Saidi Reddy and opposition Congress' N. Padmavati Reddy, wife of state Congress chief Uttam Kumar Reddy.
The bypoll was necessitated by the resignation of Uttam Kumar Reddy from the Assembly after he was elected to the Lok Sabha from Nalgonda.
The TRS has never won the seat since it was created after the delimitation of constituencies in 2009. Uttam Kumar Reddy won all three elections in 2009, 2014 and 2018.
The Bharatiya Janata Party (BJP), which has fielded Kota Rama Rao, is looking to increase its vote share, while Telugu the Desam Party (TDP), which is battling to maintain a toehold in Telangana politics, has fielded Chava Kiranmayi.
Saidi Reddy, who had lost to Uttam Kumar Reddy 7,466 votes in 2018, cast his vote at Gundlapalli village.
Tension prevailed at Uttam Kumar Reddy's house on Sunday night after TRS filed a complaint with the election authorities alleging that the state Congress chief was a non-local and should leave the constituency. Uttam Kumar Reddy, however, argued that he is a local as he has his house in the town.
The District Collector and Returning Officer Amoy Kumar said the Congress leader can remain in the constituency as Huzurnagar is one of the Assembly segments in his Nalgonda constituency, but he will not be allowed to come out of his house.
Authorities have made elaborate arrangements for smooth conduct of the bypoll, deploying nearly 1,500 personnel and 965 Electronic Voting Machines (EVMs).
Officials said about 1,500 police personnel were deployed in the constituency as part of the security arrangements.
( With inputs from IANS )