The bodies were found inside the Marfin Bank in Athens. The Greek prime minister said it was a "murderous act".
The protest became violent, with petrol bombs thrown at police who responded with pepper spray and tear gas.
Protesters are angered by spending cuts and tax rises planned in return for a 110bn euro (£95bn) bail-out for Greece.
A police spokesman said the three victims - two women and a man - were among 20 people working in the Marfin bank branch on Stadiou Avenue in central Athens when the petrol bomb was thrown.
Most of the employees managed to escape the fumes as the flames took hold, but the three found their way blocked as they tried to escape to the roof and they suffocated.
"We took 15 minutes to get to the site because it was very difficult to get there," fire brigade spokesman Panayiotis Falaras.
He said another five people were rescued from the building's balcony.source:bbc news
