For one, there wasn't a budget agreement. The budget, which President Donald Trump signed into law on Feb. 9, includes a $300 billion boost in spending on military and domestic programs.
"That budget agreement is highly stimulative. Also the risk of a government shutdown is gone. Also, we had a wage scare. Also, we had a CPI [Consumer Price Index] inflation scare. So however these minutes read, I think the Fed is more hawkish today," Kelly said.
Fears about inflation, which eats away at corporate profit margins and could force the Fed to hike rates faster than it anticipates, helped fuel the recent stock market sell-off.
Kelly said that "unless there is some shock" he expects there will be four rate hikes this year.
The market currently expects around three rate hikes for 2018, according to the CME Group's FedWatch tool.
Kelly expects this more hawkish tone to be on display in Fed Chair Jerome Powell's first semiannual address to Congress, which starts Feb. 28. Powell took the helm of the central bank earlier this month.
Danielle DiMartino Booth, president of Money Strong and a former advisor to the Dallas Federal Reserve, agreed there's a possibility there will be a "sea change in the message from the Fed when Powell goes up in front of Congress next week."
Therefore, the market may start upping the chance of more rate hikes this year, she told "Power Lunch."
— CNBC's Jeff Cox, Patti Domm and Jacob Pramuk contributed to this report.