"General Motors manufacturers the Chevrolet Cruze sedan in Lordstown, Ohio. All Chevrolet Cruze sedans sold in the US are built in GM's assembly plant in Lordstown, Ohio. GM builds the Chevrolet Cruze hatchback for global markets in Mexico, with a small number sold in the US," the company said.
Shares of GM fell 0.4 per cent to $US34.70 in premarket trading after the tweet.
Last year Trump threatened to tax Ford, which plans to shift production of the compact Focus to Mexico.
Hours after the GM threat, Ford announced that it is cancelling plans to build a $US1.6 billion plant in Mexico and instead will boost US production of electric vehicles.
"Ford today announced it is canceling plans for the new plant in San Luis Potosi, Mexico," the company said in a statement.
At the same time, Ford is adding 700 US jobs and investing $700 million during the next four years to expand its Flat Rock Assembly Plant in Michigan so that it can build self-driving and electric vehicles.
One of Trump's first tweets after winning the election was aimed at Boeing, claiming he wanted to cancel the construction of the new Air Force One, falsely stating that it was costing US$4 billion (NZ$5.7b).
After his morning tweets about GM, Trump then shifted gears and attacked the Affordable Care Act, otherwise known as 'Obamacare'.
"People must remember that ObamaCare just doesn't work, and it is not affordable - 116 per cent increases (Arizona). Bill Clinton called it 'crazy'," he wrote. "The Democrat Governor of Minnesota said 'The Affordable Care Act (ObamaCare) is no longer affordable!' - and, it is lousy healthcare."
Former US president Bill Clinton was critical of Obamacare during the election campaign.
"You've got this crazy system where all of a sudden 25 million more people have health care and then the people who are out there busting it, sometimes 60 hours a week, wind up with their premiums doubled and their coverage cut in half. It's the craziest thing in the world," Clinton said.
Clinton tried to walk back the comments afterwards.
"Look, the Affordable Health Care Act did a world of good ... we, for the first time in our history, at least are providing insurance to more than 90 per cent of our people," he said.
"But there is a group of people - mostly small business owners and employees - who make just a little too much money to qualify for Medicaid expansion or for the tax incentives who can't get affordable health insurance premiums in a lot of places. And the reason is they're not in big pools. So they have no bargaining power."
- additional reporting AP.