The man died when the dome of a church that was being renovated in the town of Arkalochori caved in.
People were sent rushing out on to the streets when the earthquake struck at 09:17 (06:17 GMT).
Many buildings were damaged and some reduced to piles of rubble from the initial quake and strong aftershocks.
People who live in damaged, older buildings are being advised to stay outdoors.
Some 2,500 tents were set up to house those who could not safely return to their homes on Monday, government minister Christos Stylianidis told Greece's Ant1 news.
He also declared a state of emergency in the Heraklion region - where Arkalochori is located.
British woman Millie Mackay and her nine-year-old daughter Eleni are on holiday in Crete and were in their ground floor hotel room when the earthquake hit.
"Glasses started smashing so we ran outside by the pool," Ms Mackay told the BBC.
"There the bosses guided us to a place of safety... [The manager] was then calling out room numbers and checking if everyone was out and OK."
Local resident Evangelia Christaki told AFP news agency that she had just enough time to grab her husband, who has a disability, and run outside as her house shook.
"Fortunately, our home was not too badly damaged," she said. "But the authorities have told us to stay outdoors over the next hours. In any case, we are so scared."
The small farming town of Arkalochori, located about 30km (18 miles) from the island's capital Heraklion, was particularly badly hit by the earthquake.
Pictures from the area show damaged shop fronts and crumbled buildings.
Local media is reporting that safety inspections are now under way, with members of Greece's disaster response unit flown in with sniffer dogs and specialised rescue equipment.