Dozens of Syrians living at the Diavata centre joined the protest after the woman, who was in her late twenties, was found unconscious in a communal shower.
First aid was administered but the woman died before an ambulance arrived at the centre.
State agency ANA said the victim suffered from epilepsy.
Around 150 Syrians subsequently marched towards the nearby city of Thessaloniki in protest, demanding better health services in their state-run camp.
They temporarily blocked a local highway before returning to the migrant centre.
Over 57,000 mainly Syrian refugees and migrants from other nations are currently staying in Greek camps, trapped in the country by a series of European border closures earlier this year.
Greece's public health watchdog has warned that many of the camps in the north of the country – created out of abandoned industrial facilities and warehouses – are ill-suited as long-term accommodation.
The government says it is in the process of building other facilities to relocate the migrants from the camps in question.
Meanwhile, a recent failed coup against Turkey's Presisdent Recep Tayyip Erdogan has inched up the number of migrants arriving in Greece in the past two weeks, government figures have shown.
The average rate has increased to 90 people a day, compared to 30 before the attempted putsch, according to the data.
"For the moment, there is no concern on our part," a Greek government source insisted on Thursday.
"We are following the situation closely and are vigilant... this could be a temporary increase," the official told AFP.
At the height of the migrant crisis last year, thousands of people would land every day on Greek Aegean islands close to the coast of Turkey.
Most were allowed by Greece to continue their journey northwards, prompting an outcry among several European states that hastened to shut their borders earlier this year.
An EU-Turkey accord in March succeeded in stemming the flow, but there are fears in Greece that this deal could unravel after the failed 15 July coup.
A purge in Turkey has seen over 8,000 arrests among the army, the police and judiciary, and hundreds have lost their jobs in every major Turkish ministry.
Three days after the attempt on the government, a group of Turkish officials assigned to monitor the migration deal on the Greek side returned home, and have yet to be replaced.