The Press Trust of India (PTI) news agency broadcast images of piles of concrete, and state rescue teams with heavy digging machines searching for bodies.
The commercial building, which had been used by multiple small companies -- including as a warehouse and as a vehicle workshop -- collapsed on Saturday afternoon.
PTI quoted officials as saying eight bodies had been pulled out, and 28 people were injured.
It was not clear if there were others still trapped.
The cause of the collapse is not known, but building and construction accidents are common during India's June-September monsoon season, with old and rickety structures buckling under days of non-stop rain.
Akash Singh, who worked in the building, said a pillar had developed a crack.
He had moved to the ground floor fearful it would worsen, with lashing monsoon rains battering the city.
"Suddenly, the entire building collapsed on us," Singh said, PTI quoted him as saying.
Yogi Adityanath, Uttar Pradesh state chief minister, called the deaths "heart breaking" in a statement, and offered his condolences to the grieving families of the dead.