A statement from Ukraine's Main Intelligence Directorate said that Moscow's forces are using aircraft to move weapons and equipment out of the Middle Eastern country.
The briefing, quoted by press agency Ukrinform, predicts that Russia will lose control of its Tartus naval facility and Khmeimim Air Base following the downfall of its ally Bashar al-Assad, who has been granted asylum by the Kremlin.
Russia was reportedly given security assurances over its bases and a senior lawmaker has vowed a "harsh response" if its facilities are attacked.
Analysts from the U.S.-based Institute for the Study of War (ISW) said that the collapse of Assad's regime is a "strategic political defeat" that has "thrown the Kremlin into a crisis."
Experts added that Russia is likely to lose geopolitical influence in the Middle East and Africa if its bases, which it acquired after intervening militarily to keep Assad in power, are lost.
Rapid downfall of Russia's Syrian ally
The stunning advance of Syrian rebels, led by the Islamist Hayʼat Tahrir al-Sham (HTS), was crowned by the capture of the capital, Damascus, on Sunday.
A patchwork of insurgent groups now rules the country, which has been shattered in a civil war that has lasted nearly 14 years and pulled in major regional and world powers.
Assad's authoritarian regime had relied on Russian air prowess and Iranian support to retain control of major cities, but more recently, both countries have been tied up by conflicts with Ukraine and Israel, respectively.
"The rapid process of overthrowing the Bashar Assad regime in Syria was marked by the shameful flight of the Russian contingent from the territory of the Arab Republic," said the Main Intelligence Directorate.
Its report claimed that, on Sunday, a frigate from Russia's Black Sea Fleet and a cargo ship from its Northern Fleet left the naval base in Tartus for the Mediterranean Sea, with remaining equipment and arms being evacuated by air from the Khmeimim Air Base in Latakia province.
“After seizing Damascus, the opposition forces are advancing toward the coast, so the likely loss of Russia’s military bases in Tartus and Khmeimim will finalize the Kremlin’s defeat in the Middle East,” the Ukrainian source added.
A senior Russian politician, quoted by the privately owned Interfax news agency, said that the country would give a harsh response if its bases are attacked.
The agency has also reported that Moscow was given assurances regarding the safety of its bases as a condition of giving Bashar al-Assad and his family asylum. But military bloggers have questioned how long such a deal would be honored, as the influence of Assad's government wanes.
'Major implications' for Russia in Africa
The ISW predicted that the latest developments will have "major implications for Russia's global military footprint," especially its presence in Africa.
"Russia has leveraged its Tartus naval base to project power in the Mediterranean Sea, threaten NATO's southern flank and link its Black Sea assets to the Mediterranean Sea," it said.
"The loss of Russian bases in Syria will likely disrupt Russian logistics, resupply efforts, and Africa Corps rotations, particularly weakening Russia’s operations and power projection in Libya and sub-Saharan Africa.
"Russia could seek to leverage its presence in Libya or Sudan as alternatives, but the lack of formal agreements with these countries and insufficient infrastructure makes them inadequate substitutes.
"The collapse of Assad's regime and Russia’s inability to preserve the regime will also damage Russia’s global image as a reliable ally, threatening its influence with African autocrats whom Russia seeks to support and its broader geopolitical objective to posture as a global superpower."
Meanwhile, the three-starred flag of Syrian rebel groups has been spotted flying over the Syrian embassy in Moscow, according to Reuters.
Bashar al-Assad was in power in Damascus for 24 years, having succeeded his father as president in 2000. Hafez al-Assad had reigned since 1971.