The Nikkei index ended up 0.8% at 19,890.27.
The latest official figures showed that machinery orders rose 2.6% in March from a year earlier, and were up 2.9% from the previous month.
A weaker yen has helped to drive the country's exports and has boosted its manufacturing orders.
In Australia, the S&P/ASX 200 index closed down 1.3% at 5,659.20.
Mining giant BHP Billiton's shares led the commodities sector lower after its spin-off company South32 began trading on Sydney's stock exchange.
South32 is the result of one of the largest corporate break-ups in the industry's history and holds  Australian and South African assets including aluminium, nickel and manganese mines.
Shares in the firm closed at A$2.09, at the lower end of forecasts, while BHP's shares closed down more than 7%.
South32's chief executive Graham Kerr said the sector was facing challenging times, but that the new firm would "start life with a strong balance sheet, along with high-quality, well maintained, cash generative assets and highly talented people".
In China, shares fell after showed that house prices on the mainland had fallen further.
Hong Kong's Hang Seng index was down 1.1% at 27,508.03 in afternoon trade. The Shanghai Composite had risen initially, but then went into reverse and was down 0.24% at 4,297.01.
After trading flat for most of the day, South Korea's benchmark Kospi index closed up 0.34% at 2,113.72.
Japan's Nikkei index closed higher on Monday after machinery orders rose in March, lifting hopes that business investment could be picking up.