"We have decided to go back on our agreement with Spartak because of the current political situation between Ukraine and Russia," the club said in a statement.
"We do not think it is the right thing to do to travel to Moscow."
Russia completed the annexation of Ukraine's Crimea region last month, sparking worldwide criticism.
Spartak Moscow and Dynamo Kiev were the most successful clubs and also bitter rivals before the break-up of the Soviet Union and they were set to open the new 44,000-seat stadium.
The 'Otkritiye' Arena will also host matches in the 2018 FIFA World Cup, which will take place in Russia.
- Sports & Recreation
- Dynamo Kiev
- Ukraine and Russia