The group's Amaq news agency said a bomber wearing an explosive vest carried out the attack, which was condemned by a former local ISIS affiliate.
Deputy Inspector Police of Quetta said that Molana Abdul Ghafoor Haideri, the deputy chairman of the Pakistan's Upper House, got slightly injured after being hit by glass of broken windows of his vehicle.
The area where the explosion took place is approximately 70 kilometres from provincial capital Quetta.
Most of the people who were killed in the attack belong to Haider's party.
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A bomb exploded next to a convoy of the deputy chairman of the Pakistan Senate in Baluchistan province this evening. Police say many others are injured and rescue operations are underway.
The bombing took place near a convoy carrying Abdul Ghafoor Haideri as it left a mosque in Mastung, some 90 km from Quetta. So far no group has claimed responsibility for the attack.
Pakistan's interior minister Chaudhry Nisar has condemned the attack and demanded a detailed report from the Balochistan police.
Haideri's JUI Party has hundreds of Islamic Sunni seminaries throughout Baluchistan. However, Senate director staff Ifthikar Mughal was killed along with the the driver and two associates of the Deputy Chairman Senate. "It was all very sudden". "Broken pieces of the windshield hit me. I am injured but safe", Maulana Ghafoor told a private TV channel shortly after the attack.
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"We don't have any clear planning or strategy to deal with extremist groups", he said. Local TV stations broadcast footage showing Haideri's badly damaged auto at the scene of the attack. Rabbani said that it was suicide attack which targeted Haideri.
TV footage showed Haideri's vehicle was badly damaged.
The attack by IS may have been a warning to Haideri's hardline Jamiat-e-Ulema Islam (JUI) against participating in the country's democratically elected government, said Zahid Hussain, an expert on militancy in Pakistan.
Baluchistan, along the border with Afghanistan, has always been beset by militant violence, including by ethnic Baluch groups agitating for self-government.
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IS has stepped up attacks lately in Pakistan.