Mr Dorsey explained in a tweet that his account had been suspended in "an internal mistake".
It's not known whether @jack's account was removed as part of a wider clean-up of the social network, but Twitter has recently suspended the accounts of several users from the "alt-right" movement.
Self-described "alt-Reich queen" Tila Tequila was banned from the site yesterday after posting a photo performing the Hitler salute at a US white nationalist event.
Twitter is not the only social media outlet to experience problems from within, however.
Just two weeks ago, Facebook accidentally pronounced two million of its users were dead, posting a remembrance message to the accounts and asking visitors to "remember and celebrate" their lives.
One of accounts affected was that of its founder, Mark Zuckerberg.
Facebook issued a statement calling the issue "a terrible error that we have now fixed".
