The bomb, believed to be placed on a motorcycle with a Tamil Nadu registration plate parked between a van and a car, went off around 10.30 AM about 100 metres from the BJP office in Malleshwaram.
Karnataka Deputy Chief Minister and Home Minister R Ashoka said the attack was an act of "terror."
"It is a very clear act of terror... It is targeted at the BJP, our senior leaders and workers", he told reporters.
City Police Commissioner Raghavendra Auradkar said a motorbike with an "incendiary bomb" was used in the blast that coincided with the third anniversary of Chinnaswamy stadium blast in which several people were injured.
Sixteen people were injured -- 11 policemen and five civilians, including three women -- in the blast.
Media reports said that investigators have recovered details of the SIM card and the registration of the motorcycle on which the bomb was placed.
Union Home Minister Sushilkumar Shinde said the Centre would start an inquiry into the attack.
Speaking to reporters in New Delhi, Shinde on Wednesday said: "I came to know of the Bangalore blast and will start an inquiry into the incident."
"I will also have interaction with the Karnataka government and the police department," he said.
Intelligence officials told TV channels that an Improvised Explosive Device (IED) was used for the strike.
While the cause of the blast weeks ahead of the Assembly polls on May 5 was not known, Karnataka Director General of Police (DGP) Lalrokhuma Pachuau said the injured were out of danger.
"The National Investigation Agency (NIA) officials have come besides forensic experts. We are examining the place of occurrence minutely. We do not what is the material of bomb blast," the DGP said.
Meanwhile, Congress spokesperson Shakeel Ahmad spurred a controversy as he said the attack would help the ruling BJP in the upcoming Karnataka assembly elections.
Ahmad tweeted: "If the blast near BJP's office in Banglore is a terror attack,it will certainly help the BJP politically on the eve of election."
The BJP called Ahmad's comment as 'insensitive and inhumane'.
The BJP's Karnataka unit tweeted: "Congress Spokesperson Shakeel Ahmad's tweet on blasts in Bangalore is insensitive and inhumane."
The Congress later distanced itself from Ahmad's remark as party general secretary Janardan Dwivedi told media: "Any terror incident is a matter of concern.
"It is a national problem as well as an international problem. We see terrorism from that perspective. It is a challenge for the country," he said.
"These incidents should not be seen from the perspective of political gain or loss," Dwivedi said.
However, Ahmad refused to back down and said he had merely stated facts that were misunderstood by the BJP.
“I have made no allegations against the BJP. I have said, this has happened in front of the BJP’s office before the elections, so people will sympathize with the BJP due to which they will get the benefit of more votes,” Ahmad said.