The tweets containing racial slurs and suggestions about a bomb showed up around 2000 GMT on the @jack account of the founder of the short messaging service before being deleted.
Some of the tweets contained the hashtag #ChucklingSquad, which was believed to indicate the identity of the hacker group. The same calling card was left behind during recent hacks of other high-profile social media personalities.
The messages contained racial epithets, and included a retweet of a message supporting Nazi Germany.
Twitter said that the phone number associated with Dorsey’s account was “compromised due to a security oversight by the mobile provider”, allowing a hacker to posts tweets to @jack by sending text messages.
Dorsey’s account has been secured and there was “no indication that Twitter’s systems have been compromised”, according to the San Francisco-based internet firm.
It appeared that tweets posted on Dorsey’s account by the hacker were up for about a half-hour before they were removed.
Pinned atop Dorsey’s account was a tweet from early last year saying: “We’re committing Twitter to help increase the collective health, openness, and civility of public conversation, and to hold ourselves publicly accountable towards progress.”
A barrage of comments fired off on the platform questioned why the Twitter co-founder didn’t secure his account better, and how disturbing a sign it was that the service couldn’t keep its own chief safe on the platform.
“If you can’t protect Jack, you can’t protect … jack,” one Twitter user quipped.
The news comes with Dorsey and Twitter moving aggressively to clean up offensive and inappropriate content as part of a focus on “safety”.
“This might be the only way to get rid of racist tweets on this platform,” a Twitter user commented.