Officials say the militant detonated his explosives outside a police base in the port of Mukalla, killing recruits as they queued up outside the building.
IS's jihadist rival, al-Qaeda in the Arabian Peninsula (AQAP), was forced out of Mukalla last month by a Saudi-led military coalition.
The conflict in Yemen has displaced two million people since 2011.
Hospitals in Mukalla, capital of Hadramawt province, said they were treating at least 60 people wounded in the attack.
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Reports said the bomber had joined a queue of men lining up at the police recruitment centre before detonating his explosives belt.
A statement from IS said the bomber had been targeting "apostates of the security forces".
The bombing is the second such attack in Mukalla claimed by IS militants since AQAP's withdrawal from the city.
The group claimed a suicide car bomb attack that killed 15 soldiers last week.
The port city of 500,000 people had been held for more than a year by AQAP, which has taken advantage of Yemen's civil war to seize territory, weapons and money.
A suicide attack claimed by the Islamic State (IS) group has killed at least 31 police recruits in southern Yemen.