Elon Musk's social media outbursts could land him in some uncomfortably hot water, according to Laura Unger, a former SEC commissioner and the agency's acting chairman under President George W. Bush.

Enforcement action by the Securities and Exchange Commission is "substantially likely" against Musk, Unger told CNBC's "Fast Money: Halftime Report" on Wednesday. The SEC has broad anti-fraud authority, she said, and the power to order a cease-and-desist order, an injunction, fine or even bar officers and directors who are unfit for their office, she added.

Tesla's founder and CEO has drawn scrutiny for a tweet he made last week saying he was considering taking the electric car maker private, putting the price of a deal at $420 and adding the phrase "funding secured." The now infamous Twitter post has forced Tesla and Musk to scramble to explain.

The tweet provoked an immediate reaction in Tesla's shares on Aug. 6. The stock was falling Wednesday, down 3 percent, as worries mount about an SEC investigation into the statement.

"I would definitely want to know what he was thinking," Unger said.

The commission would be looking "certainly for misstatements and whether or not Mr. Musk intended to manipulate the market, which some people contend," Unger said Wednesday. "Certainly he was reckless in making statements regarding a price and saying there was funding and that he was taking the company private."

"I would make sure that the enforcement division was on this and was on it quickly," she said.

CNBC reported Wednesday that Goldman Sachs had been hired to advise Tesla. Musk tweeted earlier this week that he was working with Goldman and private equity firm Silver Lake.