"There were seven low-intensity explosions," he said.
"Some of them were in crowded areas. At least person was killed and 15 to 20 were injured."
Television footage showed police officers from bomb squads scouring the areas affected.
India has been struck by bombings in recent years, with targets ranging from mosques and Hindu temples to trains.
However, it is unusual for any group to claim responsibility for the attacks.
Police said that attacks bore some resemblance to the Bangladeshi group Harkat-ul-Jihad al-Islami.
Indian shares extended losses to more than 3.5 per cent on Friday, after reports of the blasts.
Bangalore, in the south of the country, is a centre for many foreign firms, outsourcing and IT.