The shooting happened around 5:30 pm (1630 GMT) outside the university city's Groninger Museum, when the man threatened bystanders with a number of large knives, police spokesman Ernest Zinsmeyer told AFP.
"When police approached the ma, he fled. Officers fired a warning shot but the man tried to stab bystanders as he ran away and police shot him," he said.
The man then fell into a canal near the museum and was pronounced dead by the time police retrieved him from the water.
He said although a terror attack could not be ruled out, it was unlikely. The incident was being investigated.
As in other countries, Dutch police have been on high alert since a series of Islamist attacks left 17 people dead in Paris earlier this month.