Republican Gov. Haley Barbour called the bill "terrible" and said it would force the state to cut spending on programs such as economic development.
"This is Congress far exceeding the authority of the federal government by forcing states to change already-adopted budgets to meet the desires of the far left," Barbour said in a news release.
President Barack Obama signed the $26 billion measure into law late Tuesday.
Two of Mississippi's congressmen, Democrats Travis Childers and Bennie Thompson, voted for the bill. Republican Gregg Harper and Democrat Gene Taylor voted against it.
Barbour said to get the federal money, Mississippi would have to spend $50 million to $75 million more than the Legislature budgeted for the fiscal year that began July 1. He said that would force spending cuts in areas such as law enforcement, human services and mental health.
When lawmakers finished writing the state budget in April, leaders said they hoped the federal government would pump more money into Medicaid, a government health insurance program for the needy.
The White House said in a news release that Mississippi's allocation for education would be $97.8 million.
Nancy Loome of the Parents Campaign, a group that promotes public education, said Tuesday that Mississippi schools badly need the federal money. Several districts have cut jobs because of the tight state budget.
"It would be a disservice to Mississippi children and their teachers to leave these funds on the table," Loome said. "Our state's leaders need to be thinking of every way possible to take advantage of any opportunity to protect the integrity of our education system."
Ed Sivak is director of the Mississippi Economic Policy Center, which advocates policies to help people with low or moderate incomes. He said Tuesday that state lawmakers should seek ways to use the federal money for education and Medicaid without cutting funds from other government services.
"With teachers losing their jobs and class sizes increasing, pulling down these resources should be a top priority for the state," Sivak said. "The worst thing we could do now is leave this money on the table."
Federal Funds Information for States