CPI fell 0.1 percent in May and was up just 0.1 percent excluding food and energy. CPI was expected to be flat but higher, up 0.2 percent, excluding food and energy.
"It means nothing for today, but if we don't see both the economy and inflation numbers firm up over the course of the summer, it will make it more difficult for them to pursue what seems to be their quest for a third rate hike this year," said Ward McCarthy, chief financial economist at Jefferies.
The 10-year yield slumped to 2.11 percent, its lowest level since Nov. 10, after the release of May CPI, which was up 1.7 percent year over year, on the core. Economists had expected a 1.9 percent level. The core CPI, before April, had been up more than 2 percent consistently since the fall of 2015.
The 2-year note, most sensitive to Fed rates, fell to 1.31 percent, after reaching an overnight high of 1.36 percent.
Fed funds futures showed a 36 percent chance for a second hike this year, down from 50 percent Tuesday, according to BMO.
"Three months in it's hard to justify it as transitory. It's pretty bad any way you slice it," said Aaron Kohli, director of fixed income strategy at BMO. "This is leaving the market still very focused on the Fed hiking today, but cutting down the prospect of future hikes and tightening more significantly."
"The market was already concerned about what was going on in inflation before today's prints," said John Briggs, head of strategy at NatWest Markets. "Even if you get a hawkish Fed, the market will look past it. The market is going to be hesitant to price in anything."
Briggs said the Fed may tweak its statement based on the data.
"I think for me it means that they're less likely to describe the declines as transitory," he said, adding the Fed can say it is confident that it will turnaround. "I don't think it's going to change the rate hike, but the tone. It's hard to see them being hawkish today."
Retail sales data for May was also disappointing, showing a decline of 0.3 percent, the largest drop since January 2016. Control retail sales, which impact GDP, were unchanged in May, but they were revised up to a 0.6 percent gain in April. That number excludes automobiles, food, gasoline and building materials.