The accident in the city of Bhiwandi, which neighbors India's financial capital Mumbai, happened around 3:40 am (2210 GMT Sunday), according to local authorities.
Emergency workers from the National Disaster Response Force (NDRF) pulled 19 people from the rubble -- including two boys aged four and seven -- to loud cheers from residents.
"Total number of deaths is 10... Rescue operations are ongoing," NDRF commandant Ithape Pandit told AFP.
NDRF director general Satya Narayan Pradhan tweeted that specialist teams and sniffer dogs were trying to rescue another "20-25 feared trapped".
An official at the Thane city authority, which oversees Bhiwandi, told AFP that more than 40 emergency workers were helping search for survivors.
Images broadcast on the NDRF's official Twitter feed showed emergency workers combing through concrete and brick rubble with electrical wires hanging over their heads.
The cause of the accident was not immediately clear, but building collapses are common during India's June-September monsoon, with old and rickety structures buckling after days of non-stop rain.