India has rushed hundreds of security personnel to a district in the south after riots saw mobs burn vehicles and pelt stones after a Hindu activist was killed.

At least 20 people were injured in the unrest on Monday, after the killing a day earlier of the member of the Hindu nationalist group Bajrang Dal in Shivamogga, Karnataka state.

Karnataka, which is ruled by Prime Minister Narendra Modi's Hindu nationalist Bharatiya Janata Party, has been on edge for several weeks after a ban on Muslim girls wearing the hijab in classrooms triggered protests and counter-protests that spread nationwide.

There was violence in Shivamogga during the activist's funeral procession on Monday even as authorities imposed curfew restrictions in the area.

Several incidents of arson and rioting were reported as angry mobs pelted stones at business places owned reportedly by Muslims.

Police fired in the air and used tear gas to control the angry crowd.

Law enforcement officials in the area — which has a long history of communal violence — said on Monday they had arrested two people and blamed old rivalries for the killing.

The victim was also an active member of a group that seeks to protect cows — sacred for Hindus — and was severely criticised for a social media post depicting a pig in a mosque.

One of the Muslim pupils in the original hijab protest in Udupi district said that her brother was attacked in a hotel on Monday, local media reported.

The state's home minister Araga Jnanendra said authorities had found no link between the violence in Shivamogga and the hijab row, according to local media.

The Karnataka high court is currently hearing appeals against the hijab ban. In an interim order, the court imposed a temporary ban on the wearing of all religious symbols in schools.

The row has heightened fears among Muslims in India, with many saying they feel under attack by the Modi government and its supporters.