"Relevant services informed me about detention of a soldier of the base," the base's commander Lieutenant Colonel Vidmantas Raklevicius told journalists.
In his words, the detained person had served in the base for about a decade and was involved with flight planning.
If true, the news would suggest the foreign power had been kept well informed of activities at the base, which is crucial to regional defense and hosts NATO's Baltic Air Policing (BAP) mission along with the Amari base in Estonia.
Earlier on Wednesday, the Lithuanian Prosecutor General's Office said that an officer of the Air Force was arrested on suspicion of providing a foreign country with information, including classified data.
Another individual - believed to be the officer's handler - is also in custody.
The identities of the detained individuals have not been released.
Defense Minister Juozas Olekas said: "I am glad to see that our system and services are functional, leaving no chances for such operations. Anyone who attempt to act against the state will be put behind bars."
This is the third case over the past two months when Lithuanian law-enforcement has reported about spying cases. Charges of spying for Belarus were recently brought against an army paramedic and a former employee of the state-run company Oro Navigacija (Air Navigation).
Russia said earlier this month that it had a secret agent in Estonia's secret police for the past 15 years.
Earlier this week, German newspaper Die Welt and Estonia's national news service ERR reported that German aircrew stationed at the Amari airbase suspected their Tallinn hotel rooms had been broken into during their stay, possibly by foreign agents.
Estonia has a record of going public with all suspicions of espionage within its security and military services, most notably in the case of Herman Simm, a high-ranking Defense Ministry official jailed in 2009 for spying for Russia.
Suprisingly, no similar cases have emerged in Latvia, suggesting that either the authorities have not disclosed information about captured spies, that they simply have never been caught or - somewhat unbelievably - that there are none.