Analysts cited comments by Polish Foreign Minister Radoslaw Sikorski, who said Russia had increased its military presence on the Ukraine border, suggesting the situation could deteriorate.
Tokyo's Nikkei fell 1.05% or 160.52 points to close at 15,159.79, Sydney dropped 0.12%, or 6.6 points, to finish at 5,512, and Seoul shed 0.27%, 5.53 points, to 2,060.73.
The benchmark Hang Seng Index fell 64.13 points to 24,584.13, while Shanghai slipped 0.11%, or 2.48 points, to close at 2,217.47. Shenzhen rose 0.39%, or 4.57 points, to end at 1,177.33.
Jakarta ended down 1%, or 50.86 points, at 5,058.23, Singapore closed down 0.22%, or 7.44 points, to 3,320.23, Kuala Lumpur fell 6.77 points, or 0.36%, to close at 1,869.92, and Manila lost 0.36% or 25.03 points to 6,948.97.
"If Poland is indeed right that Russia is about to increase its presence in the east of Ukraine, buyers of all things risk will disappear fast as this is an indefinable outcome for markets," IG strategist Evan Lucas told Dow Jones Newswires.
CMC Markets added: "The potential of an invasion in Ukraine sent investors scurrying for the exits as they find the slightest excuse to scale off profits."