The 77-year-old man killed himself in the city’s busy Syntagma Square on Wednesday morning.
Greek media reported he had left a suicide note accusing the government of cutting his pension to nothing.
Flowers have been laid at the spot where he died and tributes have been paid online.
Hundreds of demonstrators gathered in the square outside parliament on Wednesday evening, the scene of many large protests in recent months.
Violence erupted, with petrol bombs hurled at police, who fired tear gas in response.
Depression and suicides are reported to have increased in Greece as the country introduces tough austerity measures to deal with huge debts.
The man has not been officially identified but was named in Greek media as Dimitris Christoulas. He was said to be a retired chemist, with a wife and a daughter, who had sold his pharmacy in 1994.
The man shot himself in the central square just before 09:00, Athens News reports.
In the alleged suicide note, found by police and reported by Athens News, he said: “The government has annihilated all traces for my survival, which was based on a very dignified pension that I alone paid for 35 years with no help from the state.
“And since my advanced age does not allow me a way of dynamically reacting… I see no other solution than this dignified end to my life, so I don’t find myself fishing through garbage cans for my sustenance.”
Dozens of people left handwritten messages and flowers at the spot where Dimitris Christoulas killed himself.
One of the notes, pinned to the tree, read “Enough is enough”, while another said “Who will be the next victim?”
Later, as night fell, the demonstrations degenerated into clashes as activists threw rocks and petrol bombs at police, who responded with tear gas and flash grenades.
Prime Minister Lucas Papademos issued a statement calling the death “tragic”.
“In these difficult hours for our society we must all – the state and the citizens – support the people among us who are desperate.”
Government spokesman Pantelis Kapsis called the suicide a “human tragedy” but said “the exact circumstances” were unknown.
Evangelos Venizelos, head of the socialist Pasok party that holds a majority in the coalition government, called on colleagues to refrain from “political commentary” and “show solidarity and togetherness”.
Antonis Samaras, head of the conservative New Democracy party, said politicians must do more to “help Greeks escape from despair”.
Drastic austerity measures have been imposed on Greece to meet the terms of a huge eurozone financial bailout needed to save the country from bankruptcy.
Thousands of civil service jobs have been cut, taxes raised and there have been reductions in pay, benefits and pensions.
Suicides increased by 18% in 2010 from the previous year, according to Reuters news agency. The number of suicides in Athens alone rose over 25% last year.
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