There’s a nagging question on Wall Street after Tesla Inc. Chief Executive Elon Musk’s buyout tweet last week: Why did Nasdaq let trading in Tesla shares continue for more than an hour afterward?

Mr. Musk tweeted at 12:48 p.m. ET on Tuesday that he had “financing secured” for a buyout of Tesla at $420 a share, a 16% premium to the share price at the time. The remark set off a frenzy of trading in Tesla shares, even as investors were struggling to discern whether the tweet was legitimate and what precisely it meant.

It...