The U.S. currency gained more than 0.2% against a basket of currencies, as risk sentiment soured in early trading in Europe.
Markets rose last week after unexpectedly strong U.S. jobs data despite some American states reporting record new coronavirus infections.
MSCI's broadest index of Asia-Pacific shares outside Japan fell 1.3% and further away from a four-month top hit last week. Japan's Nikkei shed 2.2% and Chinese blue chips 0.9%.
The Nikkei 225 index rose 1.33 percent, or 293.10 points, to close at 22,288.14 while the broader Topix index was up 0.62 percent, or 9.55 points, at 1,558.77.
Against a basket of currencies, the dollar index was up 0.27% at 97.686 while the euro lost 0.3% at $1.1209.
All major Asian indexes were upbeat with Japan's Nikkei rising 0.1%, China's blue-chip index adding 1.7% while Hong Kong's Hang Seng index climbed 1.8%.
The benchmark Nikkei 225 index rose 0.72 percent, or 160.52 points, to 22,306.48. It lost 0.91 percent over the week.
The Nikkei 225 fell 1.22 percent, or 274.53 points, to close at 22,259.79 while the broader Topix index was down 1.18 percent, or 18.65 points, at 1,561.85.
The key Nikkei 225 index fell 0.44 percent, or 99.75 points, to 22,614.69 while the broader Topix index was down 0.34 percent, or 5.44 points, at 1,571.71.