Japan's Nikkei led declines with a 3.3% drop and dipped below 28,000 for the first time in a month, while MSCI's broadest index of Asia-Pacific shares outside Japan fell 1% in early trading.
Chinese blue chips opened 0.4% lower, and Australia's benchmark slid 1.8%.
Benchmark 10-year US Treasury yields fell to the lowest since early March at 1.4110%, while those on 30-year bonds slid as low as 1.9990% for the first time in more than four months.
The yield curve - measured by the spread between two- and 30-year yields - was the flattest since early February.
The US dollar hovered near the 10-week high touched on Friday versus major peers, following its biggest weekly advance in more than a year.
"The story of last week was arguably the one-way move in the USD, which morphed into a clear de-grossing through equity markets, with the 'value' parts of the market really getting clobbered," Chris Weston, the head of research at Pepperstone Markets Ltd, a foreign exchange broker based in Melbourne, wrote in a client note.
"It feels that the pain trade is for further strength in the USD, higher real rates, and a flatter Treasury curve, with the market continuing to see the reflation trades unwound."
Shares of banks, energy firms and other companies that tend to be sensitive to the economy’s fluctuations have fallen sharply following the Fed’s meeting on Wednesday, when the central bank caught investors off guard by anticipating two quarter-percentage-point rate increases in 2023 amid a recent surge in inflation.
St Louis Fed President James Bullard further fuelled the sell-off on Friday by saying the shift toward faster policy tightening was a "natural" response to economic growth and particularly inflation moving quicker than expected as the country reopens from the coronavirus pandemic.
Several Fed officials have speaking duties this week, including Chair Jerome Powell, who testifies before Congress on Tuesday.
The MSCI world equity index, which tracks shares in 45 nations, fell another 0.2% on Monday, extending its retreat from a record intraday high reached Tuesday.
US stock futures pointed to further selling when Wall Street reopens, easing 0.2% after Friday's 1.3% slide in the S&P 500.
In commodities, gold rebounded 0.6% to $1,773.12 an ounce on Monday, looking to snap a six-day losing streak, but still remained near the lowest since early May, pressured by a stronger dollar.
Crude oil rose for a second day, with the initial move triggered by OPEC sources saying the producer group expected limited US oil output growth this year despite rising prices.
Brent crude futures rose 46 cents to $73.97 a barrel, while US West Texas Intermediate (WTI) crude rose 55 cents to $72.19 a barrel.