The concerns in equity markets saw investors flock to the safety of government bonds.
German 10-year government bond yields fell to their lowest in nearly seven months, and other high grade euro zone bond yields also fell.
The 10-year U.S. Treasury yield had earlier fallen as low as 2.750 percent, a level last seen in early April.
U.S. junk bonds sold off sharply, with their ETFs falling 0.9 percent, the biggest decline since March 1.
A rise in short-term interest rates and a fall in the long-date yield rekindled worries of an inversion in the yield curve, where shorter-debt yields become higher than longer-term ones.
Historically, an inversion between short-yields, such as three-month and two-year yields, and 10-year yields has been seen as a fairly reliable indicator of a recession down the road.
The two-year U.S. yield stood at 2.656 percent, just 0.097 percent less than the 10-year yield.
The dollar fell against major currencies, losing ground after perceptions the Fed was more hawkish than anticipated.
The dollar fell 0.4 percent against its rivals to 96.68 and within a whisker of a 9-day low of 96.554 hit in the previous session.
"The impact of (the Fed's) decision, especially for foreign countries, depends on how much the dollar will go up," former ECB vice president Vitor Constancio said.
The euro gained 0.5 percent to $1.1429, slightly off a high of $1.14395 hit before the Fed's policy announcement.
In other announcements by central banks, Japan kept its policy settings unchanged, as expected.
Sweden's currency jumped more than one percent against the dollar on Thursday after the central bank raised interest rates for the first time in more than seven years.
Britain is also due to make a policy announcement later in the day, with analysts expecting the Bank of England to keep rates steady.