The 16-year-old boy's condition is critical and he is being treated at a hospital in the city.
The police officer who is suspected of having fired shots at the boy's head has been arrested and is off duty, the local police announce.
Around 1,500 people took part in a protest march in Thessaloniki on Monday which was said to have been organized by left-wing and anarchist groups.
Some of the protesters threw Molotov cocktails and destroyed smaller shops.
Police are reported to have responded with tear gas and stun grenades.
The demonstration ended without any arrests or reports of serious injuries.
Before that, about a hundred men, who are said to belong to the boy's family, had set up barricades and blocked access to the hospital where the teenager is being treated.
The men also set garbage cans on fire.
Even in the capital Athens, a few hundred people took part in a demonstration in solidarity with the boy.
The demonstrators also brought up a similar case earlier when a Roma man was shot by the Greek police.
"They shot them because they were Roma," read one of the banners.
Roma living in Greece, together with human rights groups, have repeatedly accused the Greek police of discrimination.