The regulator filed a lawsuit against Mr Musk, alleging he misled investors in an August 7 tweet, which indicated he had “secured” sufficient funding to take Tesla private at $420 (£320) per share.
The business magnate settled the charges with the SEC on Saturday, which forced both him and Tesla to pay $20million (£15million) and for him to step down as chairman for at least three years.
The ruling nevertheless allowed the business mogul to remain as the company’s chief executive.
Mr Musk has nevertheless shot back at the regulator, writing on Twitter: “Just want to say that the Shortseller Enrichment Commission is doing incredible work.
“And the name change is so on point.”
The business mogul was warned on Twitter not to aggravate the situation, with one user saying: “Be careful about enraging the Shortseller Enrichment Commitment.”
Mr Musk responded with a mocking statement, saying: “Sorry about the typo. That was unforgivable. Why would they be upset about their mission? It’s what they do.”
Former SEC lawyers also warned Mr Musk against making further mocking statements regarding the SEC.
However, they noted his latest remarks were unlikely to jeopardise the settlement the two parties agreed on Saturday, which prevents the business magnate from denying wrongdoing or suggesting the regulator’s allegations were untrue.
Peter Henning, a law professor at Wayne State University in Detroit, said: “I don’t think the SEC would look at this as a denial of the facts alleged.
“But you don’t take gratuitous shots at the SEC. There’s no real upside.”
Alma Angotti, former SEC enforcement official, added: “It probably doesn’t affect the settlement between Musk and the SEC, because it does not deny wrongdoing and does not seem to be material company information.”
She nevertheless warned it could affect the company, saying to USA Today: “They promised to have controls to keep him from doing these things.
“Granted it has only been three days, but it may have been sensible to ask him not to tweet anything related to the company until they had an opportunity to put in the policies, procedures and controls required by the settlement.”
In a direct attack on Mr Musk, she added: “It bolsters the SEC’s argument that he is uncontrollable.
“It also bolsters the SEX argument that the motive for the false and misleading tweets about taking the company private was to thwart short sellers.”
Mr Musk’s tweet nevertheless appeared to worry investors, with shares falling 2.4 percent in after-hours trading to $276 (£212). Shares had already fallen 4.4 percent prior to the tweet.
His settlement with the SEC was also placed in jeopardy after US District Judge Alison Nathan in Manhattan ordered him and the SEC to explain in a joint letter by October 11 why their fraud settlement was fair and reasonable and would not hurt public interest.
Judge Nathan noted it was regular practice to request such letters.
Adam Pritchard, a University of Michigan law professor and former SEC lawyer, commented on her request, saying: “She may want to know why Tesla is paying a fine because the CEO doesn’t know when to shut up.”