A suspected suicide bomber targeted civil servants at a government building in the city, witnesses said.
Emergency workers have rushed to the scene to help evacuate the wounded.
Militant Islamist group Boko Haram, which often targets northern Nigeria, has stepped up attacks since President Muhammudu Buhari took office in May.
The group has not yet commented on the latest attack.
It came a day after police chief Solomon Arase announced new measures to curb the rise in bombings. They include:
. banning street trading and hawking in the capital, Abuja
. strengthening security at all mosques and churches countrywide.
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Witnesses in Zaria said people including primary school teachers had been queuing up seeking employment under Mr Buhari's administration when the bomb detonated in Zaria's Sabon Gari district.
"We call on our citizens to be vigilant and avoid crowded places like markets, mosques, churches and motor parks in the next few weeks," Kaduna state governor Nasir El-Rufa'i said on his Twitter account.
Mr El-Rufa'i said the government was working with the security agencies to end the wave of militant attacks in the country.
More than 200 people were killed in attacks blamed on Boko Haram last week.
On Sunday two bombings in Jos, Plateau state, left at least 44 people dead.
On Monday, a young girl believed to be just 13 was killed when explosives strapped to her body detonated near a mosque in Kano city, the biggest in northern Nigeria.
Some analysts link the upsurge in bombings to Mr Buhari's decision to remove military checkpoints countrywide on the grounds that internal security was the responsibility of police, reports the BBC's Bashir Sa'ad Abdullahi from Abuja.
Plateau state governor Simon Lalong has called on Mr Buhari to reverse his decision, saying checkpoints made it more difficult for militants to move around.
Meanwhile, military spokesman Colonel Sani Usman told the BBC that 100 men, 24 women and dozens of children accused of links to Boko Haram had been freed.
Some has spent months in custody but investigations revealed that they were innocent, Col Usman added.
Regional forces have been battling Boko Haram in north-eastern Nigeria, and have recaptured all major cities and towns from the group.