The blast followed gun and bomb attacks on political figures and journalists in recent weeks.
Responsibility for some has been claimed by anti-establishment leftist groups angry about the country's financial woes.
The device, which exploded just before 11am local time, was left in a rubbish bin close to a branch of National Bank at The Mall shopping centre in the suburb of Maroussi.
While shops are closed on Sundays, cafes, cinemas and restaurants in the centre were open for business. Police evacuated the mall after two warning calls to a newspaper and a news site were made about half an hour earlier. It is believed about 200 people were in the shopping centre.
"We were doing an inventory in our shop and the police told us to evacuate. We ran out and in 10 minutes we heard the blast. It all happened really fast," a shop clerk said.
Police shut down the nearby metro station, combed the centre for other explosive devices and were checking security cameras. Authorities said the two security guards suffered minor cuts from shattered glass, and police reportedly believe the device was a makeshift time bomb.
All major political parties immediately condemned the attack, the first to cause injuries in several years.
Greece is in the sixth year of a recession that has fuelled anger against banks, foreign lenders and politicians, blamed by Greeks for bringing the country close to bankruptcy.
On Monday of last week, unidentified attackers opened fire on the Athens headquarters of Greece's co-ruling New Democracy party with a Kalashnikov assault rifle.