The blast occurred around 3.20pm local time near a bus stop," the police source said, requesting anonymity. "One man died in hospital and nine others are injured."
A bomb squad team was working to determine if the blast came from a grenade or mine, the police source said.
Pictures published by local media showed several bodies lying on the ground in the bustling Downtown district and what appeared to be blood on the pavement.
Security forces later found an unexploded grenade near the site of the blast, the police source said.
A local volunteer paramedic who arrived on the scene shortly after the explosion said his team had taken two seriously injured people to hospital.
No group has claimed responsibility.
Turmoil
The Southeast Asian country has been in turmoil since the military coup that ousted Aung San Suu Kyi's civilian government, with fighting flaring in ethnic rebel border areas and the economy in chaos.
Self-declared civilian "people's defense forces" have also sprung up to fight the junta and dissidents have targeted officials or organization perceived to be working with the military.
Across the country, there are almost daily killings of low-level junta officials or alleged informers, with details murky and reprisals from the military often following quickly.
Most of the violence has occurred in rural areas, although anti-coup fighters have also targeted officials and infrastructure in towns and cities.
And in August, anti-coup fighters shot dead five policemen on a commuter train in Yangon.
A shadow government dominated by lawmakers from Suu Kyi's ousted party said it condemned the blast on Tuesday. The group is working to overturn the coup.
"We strongly condemn this terrorist act targeting civilians," its Defence Ministry said in a statement.
More than 1,800 people have been killed and more than 13,000 arrested in the junta's crackdown on dissent since the coup, according to a local monitoring group.