Apart from the Indian Ambassador's residence, other mission staff also stay inside the premises.
"No injury reported so far," a source said in New Delhi.
The attack happened at about 11.15 am in the heavily fortified diplomatic quarter in Kabul which houses a number of embassies, according to local reports.
Streets in the city centre, especially around the Presidential Palace, the Green Zone and Wazir Akbar Khan, were largely closed off by security forces after the attack. The number of security personnel on the streets were also quickly increased.
The attack comes amid extremely tight security in the capital following last week's deadly explosions that claimed over 150 lives and coincides with the launch of the Kabul Process meeting this morning.
Representatives from at least 23 countries, including India, are participating in the meeting aimed at establishing peace in the country.