A 19-year-old youth Nagaraj was rescued from debris, police said.
All the labourers, said to be from Andhra Pradesh, were working in a private godown. Five fire tenders were pressed into service for rescue work.
The incident occurred after heavy rains lashed the area last night, police said.
Tiruvallur District Collector K Veera Raghava Rao visited the accident spot and said those responsible for the incident would be punished.
"A total of 11 people died on the spot, including four women and a child. Rescue operations are going on," Rao told reporters.