The locations include the “Red Light” prostitution district.
The measure is part of the city’s drive to contain the Covid-19 virus transmission although the Amsterdam government’s decision stands in contrast with national policy.
Last week, the national Dutch government decided not to advise the public to wear masks due to a lack of evidence that doing so effectively curbs virus transmission.
The national government’s choice to not require wearing face masks is believed to weaken adherence to physical distancing rules.
The World Health Organization has recommended using masks in areas where it is impossible to maintain social distancing since June.
Amsterdam mayor Femke Halsema ordered the measure, in agreement with health authorities, as part of an experiment to see whether they may be effective after all, as some scientific studies have found, her spokesman said.
"We do think it can have an immediate effect," Sebastiaan Meijer said. "We want people to wear masks and be aware of the pandemic, so we do think it's going to help stop the virus from spreading."
City workers on Wednesday handed out leaflets to tourists and residents, most of whom do not currently wear masks, explaining the new rules. Failure to wear a mask could lead to a fine of €95 ($112).
Like other European countries, the Netherlands is facing a spike in coronavirus cases after it eased lockdown measures on July 1.