The 38-year-old woman apparently was carrying the bomb to place outside a nearby bank in Thessaloniki early on Saturday, police said.
Several storefronts and vehicles were damaged by the explosion.
Police said the woman, whom they did not publicly identify, had a criminal record related to drugs and prostitution and had been involved in at least one robbery and thefts in the past.
The Greek police's division for organised crime is investigating the incident, while authorities are also investigating whether the woman might have had ties to extreme leftist groups.
Greece has seen occasional bombings, as well as targeted killings, attributed to various organised crime groups.
The country also has a long history of politically motivated violence dating to the 1970s, with domestic extremist groups carrying out small-scale bombings that usually cause some damage but rarely lead to injuries.
In 2024, a man believed to have been trying to assemble a bomb was killed when the device he was making exploded in a central Athens apartment.
A woman inside the apartment was severely injured.
It was unclear what their intended target might have been.
The blast had prompted Minister of Citizen Protection Michalis Chrisochoidis to warn of an emerging new generation of domestic extremists.
In April, a new group calling itself Revolutionary Class Struggle claimed responsibility for a bomb that exploded in central Athens near the offices of Hellenic Train, Greece's main railway services operator, and the planting of another bomb near the labour ministry in early February.
The explosion near the train offices resulted in limited damage to the building and no injuries.
The bombing at the train offices came shortly after the second anniversary of Greece's worst railway disaster, in which 57 people were killed and dozens more injured when a freight train and a passenger train heading in opposite directions were accidentally put on the same track.
The deadly accident sparked widespread anger and exposed severe deficiencies in Greece's railway system, including in safety systems.
Some of the relatives of the victims led mass protests against the country's conservative government on the occasion of the accident's second anniversary.
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