Firefighters who put out a blaze ignited by the blast discovered two burned bodies in the street, police spokesman Akif Aktug told the state-owned Anatolia news agency.
An injured person died later in a hospital, NTV reported.
Eighteen other people were injured in the explosion in front of a city-run business center near the gate of a historic castle in downtown Antalya, NTV said.
"The cause of the explosion is still under investigation," said Guzide Ormeci, a spokeswoman for the governor's office.
A series of ambulances rushed the injured to local hospitals.
The blast followed a Sunday night bomb attack that injured 21 people, including 10 British tourists, in the resort of Marmaris.
No one claimed responsibility for that attack but suspicion fell on Kurdish guerrillas who have staged similar attacks in the past.
Antalya is a popular resort city that attracts millions of Russian and German tourists each year.