The crush happened as tens of thousands of cricket fans gathered outside the M Chinnaswamy Stadium in Bengaluru city to celebrate the winners of the Indian Premier League, the world's most popular T20 cricket tournament.
Karnataka state's Chief Minister Siddaramaiah said the crowd tried to break one of the stadium's gates and enter to take part in celebrations.
Eleven people were killed and 33 others were injured, Siddaramaiah said, adding that most of the injured were stable and receiving treatment in hospitals.
"At a time of celebration, this unfortunate event should not have happened. We are saddened by this," he told reporters.
"No one expected this crowd," he said.
Cricket fans had come out to celebrate Royal Challengers Bengaluru's first Indian Premier League title win on Tuesday. The team had given away free passes to fans for the event through its website, and urged them to follow guidelines set by police and authorities.
The team in a statement said it was "deeply anguished."
Local TV news channels showed some people stretched out on the ground and emergency personnel carrying people into ambulances, while celebrations inside the stadium continued.
DK Shivakumar, the deputy chief minister of Karnataka state, told reporters that "the crowd was very uncontrollable."
The Board of Control for Cricket in India, which organises the IPL, icalled the incident "unfortunate."
"This is a negative side of popularity. People are crazy for their cricketers. The organisers should have planned it better," BCCI secretary Devajit Saikia said.
Indian Prime Minister Narendra Modi called the incident "heartrending" and said his "thoughts are with all those who have lost their loved ones."
Stampedes are relatively common in India when large crowds gather. In January, at least 30 people were killed as tens of thousands of Hindus rushed to bathe in a sacred river during the Maha Kumbh festival, the world's largest religious gathering.
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