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.
