Suspicious malware was found in a computer in the IT network of Kiev's main airport, Boryspil, last week.
Almost 7 million people pass through the airport every year, and a cyberattack on its digital infrastructure could have caused chaos.
Speaking to Reuters, military spokesman Andriy Lysenko said: "The control centre of the server, where the attacks originate, is in Russia."
The malware found at the airport was similar to that which targeted three major Ukrainian power firms in late December, in an attack which caused blackouts and power outages across the country.
This attack was also traced back to Moscow, after a US cyberintelligence firm found it was part of a Russian group's ongoing hacking campaign.
The airport malware was spotted early, and was disabled before it could cause any damage.
The ongoing conflict between Ukraine and Russia has given rise to what has been called a 'cyber war' - hackers from both sides have launched a number of attacks on each other, targeting government websites and military IT systems.
In March 2014, immediately after the Russian annexation of Crimea, Russian hackers disrupted the mobile phones of a number of members of the Ukrainian parliament. Shortly after, Ukrainian hackers gained access to live CCTV camera feeds in annexed regions, in order to monitor Russian troop movements. Countless other tit-for-tat attacks have been exchanged since the conflict began.
Many of these Russian cyberattacks are believed to have been connected to a malicious software platform called 'BlackEnergy' - Ukrainian authorities will now investigate whether the airport attack was linked to this platform as well.