The deactivation of President Donald Trump’s Twitter account by a rogue employee was the most public sign yet that Twitter’s greatest star can also cause the company great headaches.

Twitter blamed the incident—which took Mr. Trump’s @realdonaldtrump account offline for 11 minutes late Thursday—on actions taken by a customer-support employee on his or her last day of work. Twitter said it was taking measures “to prevent this from happening again.”

Inside Twitter, the brief deactivation elicited celebration or amusement even in the upper ranks. A couple of hours after the deactivation of Mr. Trump’s account, Twitter Chief Executive Jack Dorsey liked a tweet with an image of his face superimposed on celebrity painter Bob Ross standing before a canvas depicting Mr. Trump’s deactivated account. “There are no mistakes, only happy little accidents!” the caption said.

A spokesman for Twitter declined to comment.

Like many tech companies, Twitter’s workforce is young and concentrated in the left-leaning Bay Area. Employees of Twitter donated $4,060 to Mr. Trump’s campaign from 2015 to 2016.