Responding to an audience question at a town hall at his presidential center in Atlanta, Carter said Tuesday that Wilson's outburst was also rooted in fears of a black president.
"I think it's based on racism," Carter said. "There is an inherent feeling among many in this country that an African-American should not be president."
But Wilson's son disputed that.
"There is not a racist bone in my dad's body," said Alan Wilson, an Iraq veteran who is running for state attorney general in South Carolina. "He doesn't even laugh at distasteful jokes. I won't comment on former President Carter, because I don't know President Carter. But I know my dad, and it's just not in him."
"It's unfortunate people make that jump. People can disagree -- and appropriately disagree -- on issues of substance, but when they make the jump to race it's absolutely ludicrous. My brothers and I were raised by our parents to respect everyone regardless of background or race."
Carter, a Democrat, said Joe Wilson's outburst was a part of a disturbing trend directed at the president that has included demonstrators equating Obama to Nazi leaders.
"Those kind of things are not just casual outcomes of a sincere debate on whether we should have a national program on health care," he said. "It's deeper than that."
Wilson's spokesman was not immediately available for comment.
Wilson, a South Carolina Republican, was formally rebuked Tuesday in a House vote for shouting "You lie!" during Obama's speech to Congress last Wednesday.
The shout came after the president commented that illegal aliens would be ineligible for federal subsidies to buy health insurance. Republicans expressed their disbelief with sounds of disapproval, punctuated by Wilson's outburst.
Tuesday's rebuke was a rare resolution of disapproval pushed through by Democrats who insisted that Wilson had violated basic rules of decorum and civility. Republicans characterized the measure as a witch hunt and Wilson, who had already apologized to Obama, insisted he owed the House no apology.
South Carolina's former Democratic Party chairman also said he doesn't believe Wilson was motivated by racism, but said the outburst encouraged racist views.
"I think Joe's conduct was asinine, but I think it would be asinine no matter what the color of the president," said Dick Harpootlian, who has known Wilson for decades. "I don't think Joe's outburst was caused by President Obama being African-American. I think it was caused by no filter being between his brain and his mouth."
Harpootlian said he received scores of racial e-mails from outside South Carolina after he talked about the vote on Fox News.
"You have a bunch of folks out there looking for some comfort in their racial issues. They have a problem with an African-American president," he said. "But was he motivated by that? I don't think so. I respectfully disagree with President Carter, though it gives validity to racism."
On Wednesday, Republican National Committee Chairman Michael Steele accused Democrats of using the race issue to shift attention away from the health care plan.
"President Carter is flat out wrong. This isn't about race. It is about policy," Steele said in a statement.
Carter called Wilson's comment "dastardly" and an aftershock of racist views that have permeated American politics for decades.
"The president is not only the head of government, he is the head of state," said Carter, who was awarded the Nobel Peace Prize in 2002 for his work to promote human rights and resolve international conflicts. "And no matter who he is or how much we disagree with his policies, the president should be treated with respect."
As president, Carter appointed record numbers of women, blacks, and Hispanics to government jobs. Under The Carter Center, Carter and his team of experts work to resolve conflict and promote democracy, among other goals.
Wilson, a former state senator elected to Congress in 2001, is known as a mild-mannered lawmaker with hard-line conservative views. But he has been confrontational in the past.
In 2003, Wilson called it "unseemly" and a "smear" for the mixed-race daughter of Sen. Strom Thurmond, Essie Mae Washington-Williams, to identify the longtime South Carolina senator as her father after his death.
After a public outcry, he reversed course and said he had the utmost respect for Washington-Williams.
As a state senator, he was an outspoken opponent of efforts to remove the Confederate flag from atop the South Carolina Statehouse.