The company closed its Moscow office and paused investment in Russia in March, following the invasion of Ukraine.
However, its 22 hotels in the country are owned by third parties and remained open.
Marriott said the process of suspending operations in Russia was "complex".
But in a statement, it said: "We have come to the view that newly announced US, UK and EU restrictions will make it impossible for Marriott to continue to operate or franchise hotels in the Russian market."
