Equity markets in China and the Philippines fell more than 1.5%, while in South Korea they were about 1% lower.
Earlier on Monday, Asian shares were broadly higher after the mammoth US stimulus bill cleared the Senate over the weekend, boosting optimism about the global economic recovery.
A spike in oil prices past $70 for the first time since the pandemic, though, sparked some worries about inflation for energy-hungry Asia.
Broadly, rising prices had already been on investors' minds, pushing US bond yields higher and keeping pressure on Asia's bond markets and equity valuations.
"The last thing anyone wants in a recovering global economy is higher oil prices," said Stephen Innes, the chief global markets strategist at axi.
"We are likely nearing a point when higher oil prices become a negative rather than a positive influence over risk assets via the inflation throughput to higher yields."
The region's currencies came under pressure as the dollar firmed on the back of stronger-than-expected jobs data and the pandemic relief bill, on top of higher oil bills.
South Korea's won fell 0.6%. On the other end, Singapore stocks jumped 2% to their highest in more than a year, led by a rally in Jardine Strategic and Jardine Matheson, which climbed nearly 20% and 14%, respectively.
Jardine Matheson said it plans to buy the remaining 15% of Jardine Strategic that it does not already own for about $5.5 billion to simplify the structure of the sprawling Asian conglomerate that has a foot in construction to aviation.
In Malaysia, shares jumped 1.5%, with Petronas Chemicals Group the biggest gainer.
The petrochemical product maker jumped close to 10% after CGS-CIMB upgraded the stock to "Add" and raised its price target. Indonesia's shares and the rupiah dipped.
The country is susceptible to higher US yields given that the South-East Asian nation houses some of the highest-yield debt in emerging markets.
The yield on Indonesia's 10-year bonds shot up 18.4 basis points to 6.809%. - Reuters