Attackers placed flaming gas canisters at three homes of local figures from the governing party in the northern city of Thessaloniki before dawn on Tuesday, causing explosions.
Vagia Nestora, the 72-year-old mother of New Democracy candidate Afroditi Nestora, died of organ failure after suffering burns that covered 80 per cent of her body, a hospital statement said.
The candidate also suffered burns and three other people were wounded.
There was no immediate claim of responsibility for the attacks, the first time in more than a decade that a person was killed in an attack targeting Greek politicians.
Greece has a decades-long history of political violence, including bombings and arson attacks, but assassinations became rare 20 years ago after leaders of left-wing militant groups were jailed.
"Yesterday we witnessed an extreme co-ordinated murderous attack against three New Democracy officials in Thessaloniki," government spokesperson Pavlos Marinakis said.
"This terrorist act was a cowardly act by extreme exponents of violence who operate under the guise of a so-called ideology against three people simply because they do not agree with their ideology," he said.
"The message we are sending is clear: terrorism will not win! No one will be afraid."
The New Democracy party and its youth branch, ONNED, called for a rally to honour the victim and protest against such attacks on Thursday evening outside the hospital where the woman died.
"We are not afraid of you," it said in a statement, saying its members stand "united against terrorism".
A police anti-terrorism unit has taken charge of the investigation into the incidents.
