The incident occurred behind Atlandara area around 4.30 am, catching the sleeping occupants unawares, said H J Tapariya, chief fire brigade officer of the Vadodara Municipal Corporation.
As many as 14 families were staying in the building.
"Rescue and relief operations are going on in full swing. It is difficult to ascertain the exact number of people trapped under the debris. A few people, including a minor girl, have been rescued from the site so far," Vadodara Mayor Bharat Shah said.
The building was constructed by the Vadodara Development Authority, officials said.
Vadodara Municipal Commissioner Manish Bhardwaj and Police Commissioner Satish Sharma are overseeing the rescue operation. Army and National Disaster Response Force teams have arrived to assist the fire brigade in the rescue work.
The injured have been rushed to a local hospital for treatment.
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