The bomber hit the main checkpoint on the way to the provincial government headquarters in the northern city just before noon (0900 GMT), provincial council spokesman Hamza Hamed said.
The attack killed four people, two of them police, and wounded 29, Saman Barzanchi, the director general of the Arbil health department, told AFP.
A crowd of onlookers gathered at the site of the blast, which broke car windows, scarred vehicles with shrapnel and left glass and debris scattered across the blood-stained street.
In that attack, the asayesh said a suicide bomber detonated explosives at the entrance to their headquarters, after which they killed four more would-be bombers before a fifth blew up an ambulance rigged with explosives.
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"When you are visiting Arbil, there is absolutely no sense of danger," said Bruno Retailleau, a French senator who was at the Arbil provincial headquarters minutes before the blast.
"Retroactively, it's chilling," Retailleau, who was heading a delegation that delivered 10 tonnes of aid for displaced Iraqis, told AFP.
There was no immediate claim of responsibility for the today's attack, which rocked a usually crowded area close to the city's main landmark, the UNESCO-listed Arbil citadel.
But suicide bombings are usually carried out by Sunni extremists in Iraq, including a series of blasts claimed by the Islamic State jihadist group in recent weeks.
Kurdish security forces are battling IS, which spearheaded an offensive that has overrun large areas of Iraq since June, making it a more prominent target for militants.