According to private television, STv, Amurrane was caught by three bullets as he visited a chemistry lab in the city on Wednesday afternoon.
An unnamed official of his Mozambique Democratic Movement (MDM) confirmed that the mayor died on the spot after the gunmen fired repeatedly at him.
The motive for the killing is not yet known.
Amurrane's MDM had won Nampula city and three of the nation’s four largest cities in local elections in 2014.
Due to its showing in those elections, the party emerged as a credible challenger to the ruling Frelimo party in presidential and parliamentary polls due in 2018 and 2019 respectively.