Siddique, a former local minister, was a senior figure in the politics of Maharashtra state, which is expected to hold legislative polls next month.
In February he defected from Congress, India's main opposition party and joined the unrelated regional National Congress Party (NCP), which is part of the governing coalition of the BJP.
Maharashtra's deputy chief minister Ajit Pawar, from the same party as Siddique, said he was shocked by the "cowardly attack".
Siddique was known for lavish parties and for close ties to Bollywood superstars.
The shooting happened with high security in place due to a major Hindu festival in the city.
Opposition parties have criticised the government, saying there was a major lapse in security. The state government has promised a thorough inquiry.
Though two suspects have been taken into custody, the motive is not clear. Police are searching for a third suspect.
Some Indian media report the suspects have said they were from a gang run by notorious criminal Lawrence Bishnoi.
Bishnoi is currently serving a jail sentence for his involvement in several high-profile murder cases, including the killing of the Indian rapper Sidhu Moose Wala in 2022.
The shooting came weeks after Siddique's security detail was upgraded following death threats.
