The new healthcare law requires U.S. citizens to either purchase insurance or pay a penalty. It exempts those who can't afford a policy.
Many uninsured people could afford coverage but would rather spend their money on something else, Gingrich said.
"And then you and I and everybody else ends up picking up for them," he said Sunday. "I don't think having a free-rider system in health is any more appropriate than having a free-rider system in any other part of our society."
The federal government has used basically the same cost-shifting argument to defend the mandate in court. But on Monday, Gingrich said he would repeal the requirement.
"I am against any effort to impose a federal mandate on anyone because it is fundamentally wrong and, I believe, unconstitutional," Gingrich said in his YouTube video.
Potential 2012 GOP rival Mitt Romney has defended a similar mandate he enacted as governor of Massachusetts by saying that states have the power to impose a coverage requirement, but the federal government does not.