Cyclone Chapala generated large waves that hit the coast, destroying dwellings and fishing boats and cutting off roads, local official Abdullahi Hashi said.
He said nomads staying in eastern Puntland were the worst affected by the storm, which hit the region beginning Sunday and is continuing.
No deaths have so far been reported. Hashi called for emergency aid for the victims.
Chapala originated in the Arabian Sea and has been battering Yemen.
Cyclones are rare in Somalia, but Puntland was also hit by the nation's deadliest cyclone,
which killed at least 300 people in 2013 and left hundreds more missing.
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