Taliban interior ministry spokesman Qari Saeed Khosti said authorities were collecting details of the explosion, which took place days after a suicide bomb attack on a Shi'ite mosque in Kunduz.
Provincial police spokesman Jamal Naser Barekzai blamed the Taliban for the attack, although the militants denied responsibility.
Afghan Ambassador to India Farid Mamundzay said Siddiqui was killed in Kandahar on Thursday night while being on an assignment.
Afghanistan's Tolo News channel cited sources as saying that Siddiqui was killed in Spin Boldak district of Kandahar.
The Taliban, who claimed responsibility for the bombing, has carried out nearly daily attacks since peace talks with the United States collapsed earlier this month.