No serious injuries were reported.
Three paramilitary soldiers suffered splinter injuries as two bombs exploded on Monday in quick succession 100 metres from the main entrance of the Bakshi soccer stadium in Srinagar, said Muneer Khan, senior superintendent of police.
A third explosion was reported in the village of Pattan, 35km north of Srinagar, but no one was injured, police said.
Hizb-ul Mujahideen, Kashmir's biggest Muslim insurgent group, claimed responsibility for the Srinagar blasts in a telephone call to local news agency, Current News Service.
At the time of the blasts, thousands of people had gathered inside the stadium to mark the 57th anniversary of India's independence.
The 15-year insurgency in Kashmir
has claimed over 66,000 lives
Jammu-Kashmir's top elected official, Chief Minister Mufti Mohammed Sayeed, was set to arrive at the stadium an hour later to hoist the tricolour national flag. Sayeed still intended to attend the ceremony, Khan said.
Television reports showed security officials trying to calm the crowds inside the stadium.
"The blasts were powerful, but no major injuries were reported," Khan said.
K Srinivasan, a senior military intelligence official in India's Jammu-Kashmir state, said security forces had prior information that Pakistan-based Lashkar-e Tayyaba group and two other groups would try to sabotage the celebrations.
Tayyaba is the fiercest among more than a dozen groups, which have been fighting security forces in India's portion of Kashmir for the region's independence or its merger with mostly Muslim Pakistan.
The 15-year insurgency has claimed more than 66,000 lives.
The groups have called for a boycott of Monday's celebrations.