The US said it added added 211,000 jobs to its economy, which was slightly better than expected.
Analysts said the numbers would make it more likely for the US Federal Reserve to raise its lending rates this year.
Japan's Nikkei 225 was up nearly 1.5% in early trade, but lost some ground later to close up 0.99% at 19,698.15.
Chinese shares traded mixed as investors were cautious ahead of a series of economic data out this week.
Hong Kong's Hang Seng index finished down 0.2% at 22,203.22, while the Shanghai Composite index ended up 0.3% at 3,536.93.
Trade figures are due on Tuesday, followed by inflation on Wednesday and then foreign investment, factory production and retail sales on Saturday.
Investors will be looking for signs of whether growth in the world's second largest economy will hit the government's target of about 7% this year, which is already the lowest in a quarter of a century.
Shares of the Liaoning-based Bank of Jinzhou closed up 9.4% after the lender made its debut on Hong Kong's stock exchange.
The bank raised close to $800m (Â£530m) from investors in its initial share offering.  It's the second time the lender has tried to list this year. Its first attempt was delayed over concerns about its ties to the controversial solar equipment maker, Hanergy.
In Australia, Sydney's S&P/ASX 200 index closed flat, up just 0.08% at 5,155.70, after being up more than 1% in early trade.
On Monday, Spanish infrastructure firm Ferrovial made an all-cash takeover bid for the Australian detention centre operator Broadspectrum - formerly Transfield Services.
The takeover offer values the firm at 715m Australian dollars ($524m; Â£347m) and saw Broadspectrum's shares rise more than 50% on the news. They finished up 47.65%.
Elsewhere, after a positive start, South Korea's Kospi index closed down 0.54% at 1,963.67.
Asian shares lost some steam on Monday despite a positive start, following a solid jobs report from the US on Friday.