Linkevičius said he addressed the incident with his Estonian counterpart, Urmas Paet, and was told that the abductors did not wear uniforms.
The minister expressed certitude that the incident occurred on the same day as the NATO summit for a reason.
"We are already used to all types of test. I believe there is a reason why this occurred on the day of the NATO summit. It is an arrogant provocation. We have to wait for an official reaction of the Russian administration. It is a reminder for us to stay alert," Linkevičius told BNS in a telephone interview from Wales on Friday.
Estonian internal security police reported that unidentified persons from Russia abducted its officer in the Estonian territory next to the Luhamaa checkpoint at about 9 a.m. on Friday.
The officer whose duties included prevention of cross-border crimes was detained at a gunpoint.
Before the abduction, radio communication was interrupted, followed by a smoke grenade from the direction of the Russian territory, Tallinn said.
Estonia has summoned the Russian ambassador over the incident.
On 27 May Lithuanian government has allowed renewing more flights to Germany and the Netherlands .