Barra served on the Strategic and Policy Forum which consisted of more than a dozen CEOs and business leaders.
The move came after the heads of 3M CEO and Campbell Soup resigned from the manufacturing council earlier in the day.
CNBC is reporting that the members of the President's Strategic and Policy Forum-a group that included representatives from GM, Walmart, Pepsi, Boeing, and a number of top financial firms-have chose to dissolve their group in the wake of Donald Trump's remarks defending the white supremacist rally/riot in Charlottesville, Virginia, last weekend.
The Twitter announcement marked a stunning collapse for the two panels, the Manufacturing Jobs Initiative and the Strategic and Policy Forum.
Update 8/16/17 2:05pm ET: General Electric CEO Jeff Immelt released a statement calling Trump's statements "deeply troubling" and expressed no confidence in the goal of the president's manufacturing council.
On June 1, Tesla Inc (NASDAQ: TSLA) CEO Elon Musk dropped out following Trump's decision to withdraw the US from the Paris climate accord. But by Wednesday afternoon, Trump had made a stunning about-face.More news: Trump drops plan to create infrastructure council: White House
According to three executives with knowledge of the discussions, Trump's startling press conference Tuesday at Trump Tower spurred the members to talk about a response. Shortly after, Trump tweeted that he was disbanding the two groups.
"We joined this council with the intent to be a voice for working people and real hope that it would result in positive economic policy, but it has become yet another broken promise on the president's record".
The group's president, Richard Trumka, and deputy chief of staff, Thea Lee, said they "cannot sit on a council for a president who tolerates bigotry and domestic terrorism".
Meanwhile, companies involved with the manufacturing group were releasing statements that distanced themselves from Trump.
"This calls into question the ability of the Trump administration to get anything done in terms of tax and infrastructure reforms", said John Doyle, director of markets at Tempus Consulting.
Jeff Immelt, chairman of General Electric and formerly a part of the Manufacturing Council, said in a statement that he too had resigned on Wednesday morning and cited Trump's statement as the reason he chose to step down.