Construction of the 50 meter (164 ft) collapsed section had been completed in February, but work on the bridge was ongoing, confirmed Varanasi commissioner Deepak Agarwal.
Police and rescue workers launched an immediate relief operation, recovering bodies from cars and a three-wheeled rickshaw, Agarwal said. Other victims were also pulled from sections of a bus.
Images of the incident, which occurred in the city's Englishia Line road area, showed at least four cars completely crushed under the weight of concrete blocks, some with people still visibly trapped inside.
India's prime minister Narendra Modi has tweeted his condolences, saying "Extremely saddened by the loss of lives due to the collapse of an under-construction flyover in Varanasi. I pray that the injured recover soon."
A technical team from Lucknow, the state's capital city, will examine the site to determine what caused the collapse Agarwal said. Police are also opening a formal investigation into the Uttar Pradesh State Bridge Corporation, a public sector company.
In a similar incident in 2016, 24 people died when a section of a overpass collapsed in the eastern city of Kolkata. The owners of the company behind its construction faced charges of attempted murder, mischief and criminal conspiracy.
The state government is giving families 500,000 rupees compensation($7,600) for those who lost their lives and 200,000 ($3,000) for those who are injured, officials confirmed.
Rescue operations were called off at 10 p.m. Tuesday, confirmed Sanjay Kumar, the Uttar Pradesh State Disaster Management Authority Commissioner. Sections of collapsed concrete had also been removed.