Al-Suneidi later died from head wounds, a doctor at al-Mansoura hospital in the port city of Aden said.
Outside the port of Mukalla in the southern province of Hadramaut, Ahmed Madi, a local council member, said one person was killed when police fired at a demonstration.
The situation was tense in other towns, including Lahij, Abyan and Dhaleh.
Early this week thousands took to the streets to mark the defeat of southern secessionist forces in 1994, shouting anti-government slogans and calling for the south to break away.
The government has blamed the unrest on southern rebels demanding secession, but many in the impoverished south have been protesting against bad living conditions.
There have been sporadic clashes between police and protesters in the south over the past few months, leaving at least 18 people dead, including five policemen, since late April.