They say the gunmen were shot dead by the security forces soon after the bomber detonated his device.
Medics told the BBC that at least nine people were injured. Consular officials said none of their staff were hurt.
Jalalabad is often targeted by Taliban militants.
A suicide bomber killed at least 13 people in the city in January.
That attack took place at the home of a prominent local politician who backed President Ashraf Ghani's peace talks.
It took place a few days after a gun battle near the Pakistani consulate in Jalalabad in which at least seven Afghan security personnel were killed.
Jalalabad is the capital of Nangarhar province, where two districts are controlled, or at least influenced, by the Islamic State group - a rival of the Taliban.
In the violence on Wednesday, police say a bomb in a car driven by one of the attackers was detonated near the Indian consulate, destroying other cars and shattering doors and windows.
In the aftermath there was a gun battle between gunmen accompanying the bomber and security forces, witnesses said. So far no group has claimed the attack.
The Afghan government has been locked in a bloody conflict with Taliban militants for more than a decade.
The Taliban have launched several high-profile attacks in recent months. The army recently said the militants were on the verge of capturing the key district of Sangin in Helmand province.
On Wednesday at least 25 people were killed in two suicide attacks in the capital Kabul and in the eastern province of Kunar.
In September, the Taliban briefly overran the northern Afghan city of Kunduz, in one of their biggest victories since they were ousted from power in 2001.
An attack near the Indian consulate in the Afghan city of Jalalabad has left five militants dead, including a suicide bomber whose device killed only himself, police have told the BBC.