The service said in a statement that the material could be obtained only as a result of a nuclear reactor's operations but did not say when it had been discovered at Moscow's Sheremetyevo international airport.
The material triggered an alarm in the airport's radiation control system and a luggage search led to the discovery of 18 pieces of the radioactive metal packed in individual steel casings, it said.
The passenger boarded the plane for Tehran and left Russia, the customs service said. It added that the passenger was Iranian national. Russian law enforcement agencies opened criminal investigation into the incident.
Sodium-22 can be used for calibrating nuclear detectors and in medical equipment, nuclear experts said.
"There is no weapons aspect to this (material)," said Research director Lars-Erik De Geer of the Swedish Defense Research Institute.
Tension is rising between Western powers and Iran after a United Nations nuclear watchdog report last month that said Tehran appeared to have worked on designing a nuclear weapon, and that secret research to that end may be continuing.
Russia, which built Iran's first nuclear power station, has said it might help Tehran construct more atomic plants.
There was no immediate comment from the International Atomic Energy Agency on the incident and whether Russian authorities had reported it to the Vienna-based U.N. body.