Japan's benchmark Nikkei 225 lost 1.09% on Tuesday to close at 21,583.12 points.
The index was pulled lower by auto giants Nissan and Mitsubishi following the arrest of Carlos Ghosn, head of the Nissan-Renault-Mitsubishi alliance.
Nissan lost more than 5.45% and Mitsubishi lost 6.85%.
Elsewhere, Hong Kong's Hang Seng was down 1.9% in late trade, while the Shanghai Composite was down more than 2%.
In Australia, the S&P/ASX 200 lost 0.38% to finish at 5,671.8 points.