Lieutenant Colonel Vasily Khitryuk allegedly passed state military secrets to the Baltic country's security services, the FSB said.
"The suspect used his former colleagues and friends who serve in the Russian army and security-related agencies" to obtain confidential information, the service said in a statement.
"Following orders from a Lithuanian intelligence officer, he [Khitryuk] offered them monetary rewards for supplying him with copies of secret documents," the statement said.
The FSB said that during Khitryuk's arrest, officers seized computer storage devices with files containing top-secret information on the combat readiness of the Baltic Fleet and Russia's military contingent in Kaliningrad.
The service said it had gathered enough evidence to launch a criminal investigation.
The Embassy of Lithuania in Moscow refused to comment on the arrest. "We do not comment on such information," an embassy official said Tuesday.
