"It's odd given the nature of this settlement. If there is a class action, it's common. But just for SEC enforcement action, particularly with a big fine, it's unusual," he said.

Former federal prosecutor Jay Hulings said the order was unusual, "but not unheard of."

The judge gave them a week to submit a joint letter explaining why she should approve it. Tesla's stock was down 5.4 percent in midday trading to $278.75 a share.

U.S. District Judge Alison Nathan said the court needs to make a "minimal determination of whether the agreement is appropriate" before she would sign off on the deal. She said the law requires her to determine whether the enforcement action is "fair and reasonable, with the additional requirement that the public interest not be disserved."

Tesla CEO Elon Musk 's settlement with the Securities and Exchange Commission hit a snag Thursday after the federal judge charged with approving it asked them to justify the agreement.

Musk and the SEC reached a settlement on Saturday, just days after the agency filed a lawsuit alleging that Musk misled investors about having the funding necessary to take Tesla private. Both Musk and Tesla will have to pay $20 million, and Musk will be required to step down as chairman for at least three years, but he will retain a seat on Tesla's board.

Charles Elson, director of the Weinberg Center for Corporate Governance at the University of Delaware, said the delay in reviewing the case is not unusual.

But what the court will do is an open question, he said. Federal courts have rejected SEC settlements in the past if the judge thinks they're too lenient.

"The court is perfectly within its jurisdiction to throw a settlement out," he said.

Often, courts will require stricter terms to approve the settlement. For example, the court could require Musk to step down from Tesla's board entirely, which would be a good move, Elson said.

"I am a little disappointed they didn't require him to leave the board," he said. "I understand the argument for not replacing him as CEO, but I certainly don't think he should be overseeing himself."

Musk's Aug. 7 tweet saying he was thinking about taking the electric car maker private at $420 a share and had "[f]unding secured" sent the stock soaring 11 percent, near an all-time high, that day to $387.46. Tesla's lost about 28 percent of its value since then. The SEC said Musk knew he didn't have the financing lined up and misled investors.

Though the deal settled the SEC's case, the Justice Department reportedly still has an open criminal investigation. Numerous shareholder lawsuits also have been filed against the company and Musk in recent weeks.

Tesla separately on Thursday said it's going to start publishing quarterly crash and safety data.

WATCH: Three experts on the future of Tesla after Elon Musk settles with SEC