The government said it closed the site, and the Inca Trail hike leading to it, to protect tourists and citizens.
Hundreds of people, mostly foreigners, are currently thought to be stranded at the foot of the site.
Dozens of people have been killed in weeks of violent protests, which began after the previous leader was ousted.
The stranded tourists at Machu Picchu are not the first to be stuck there during the protests, which have disrupted transport services and damaged nearby train tracks.
Rail services to the site were suspended on Thursday.
Last month, the authorities had to rescue hundreds of tourists nearby who had been stuck for days.
Machu Picchu is a 15th-century Incan citadel in the Andes mountains that was named one of the New Seven Wonders of the World in 2007. It is hugely popular with tourists, with around a million people visiting every year.
Some visitors arrive at Machu Picchu via the Inca Trail, which is a famous multi-day hike.
In a statement, Peru's culture ministry said that those who had already bought tickets for Machu Picchu would be able to use them for one month after the end of the demonstrations, or else refund them.
Demonstrators in Peru are demanding fresh elections and calling for the new President, Dina Boluarte, to stand down, which she has so far refused to do.
They want her left-wing predecessor, Pedro Castillo, who is in prison and who has been charged with rebellion and conspiracy, to be released.