JOIN USAngamali police station has registered a case against Joseph's driver.
Joseph told IANS that he was heading to the Kochi international airport to catch a Delhi flight to join the group of ministers led by Chief Minister Oommen Chandy when the accident took place late Sunday.
He blamed poor lighting on the road for the accident.
"There were hardly any street lights and my driver, despite his best efforts, could not do anything because the pedestrians made a hurried crossing on the highway," said Joseph.
"As soon as the accident occurred, the three pedestrians was rushed to a hospital in my car," the minister added.
George and Vijayan, both of them construction workers, succumbed to their injuries while Thomas Abraham survived.
"He is out of danger and will be discharged now," said local legislator Jose Thettayil, who happened to be coming behind in a car when the accident took place.
Joseph, who is expected to reach Delhi later in the day, said: "We will see what best can be done for the victims' families."