Snowden's lawyer claims he faces persecution from the U.S. government if he returns to American soil and that he could face torture or death.
WikiLeaks and Russia's Federal Migration Service both confirmed the application request. The service is required by law to consider the application within three months, but could do it faster.
Temporary asylum means political refuge for one year. However, that time period could be extended later.
Snowden said last week that he wants temporary asylum in Russia while he waits for safe passage to Latin America.
Snowden has been stuck in Moscow since he arrived there on a flight from Hong Kong on June 23. The Obama administration has charged Snowden with espionage and revoked his passport.
The Associated Press contributed to this report.