One of the eyewitnesses told The Anadolu Agency that the charge was planted in the car of leading vigilante Wadah Rajeh and that it went off when he was driving the vehicle on one of the streets of Zinjibar, the largest city in Abyan.
Another man – who happened to be in Rajeh's company at the time – was injured as well, the eyewitness said.
Yemeni authorities have not yet commented on the incident, for which nobody has claimed responsibility either.
Al-Qaeda, which is said to be powerful in Yemen, usually claims responsibility for such bomb attacks.
The source said blast victims had been taken to hospital to receive treatment.
Yemen's vigilante groups mostly consist of tribal militants who assist the government in fighting Al-Qaeda.
Yemen has been in turmoil since a popular uprising in 2011 ousted long-standing President Ali Abdullah Saleh a year later.