President Sebastián Piñera said the decision had caused him "pain" but his government needed "to prioritise re-establishing public order".
The COP25 climate summit was scheduled for 2 to 13 December, while the Apec trade forum was next month.
The UN said it was now looking at alternative venues.
World leaders were to gather at this year's Conference of the Parties (COP) to discuss the implementation of the Paris Accord - a landmark international climate agreement, first signed at COP21 in December 2015.
This is the first time a country has pulled out of hosting the conference at such short notice.
The demonstrations were originally triggered by a now-suspended rise in the price of metro fares in Santiago.
However protesters are now marching to express their discontent over a wide variety of problems ranging from inequality to the high cost of healthcare.
The decision comes amid a number of global climate protests, including a week of strikes led by environmental activist Greta Thunberg last month.
And as the news was announced, a US-based organisation also separately revealed that tens of millions more people than previously thought were at risk of coastal flooding from climate-driven sea-level rise within the next century.
In a statement, the UN's climate change executive secretary, Patricia Espinosa, said: "Earlier today, I was informed of the decision by the government of Chile not to host COP25 in view of the difficult situation that the country is undergoing. We are currently exploring alternative hosting options."