Watson, who has more than 65,000 followers on the site, made the admission after the intern sent a tweet on @tom_watson.
The intern wrote: "I should log out of my Twitter so that my intern doesn't twit-rape me..."
Realising the error, she quickly posted: "My boss is in a meeting, I've made a terrible mistake, I'm very sorry everyone, it wasn't meant to be offensive! logging him off now! sorry!"
The Labour deputy chairman, who was digital engagement minister under Gordon Brown, tweeted: "I sincerely apologise for the recent tweet. A lesson learned for a young intern. She's also very sorry. I will deal with the matter offline."
After the exchange, the hashtag #SaveTheIntern started trending on the microblogging site.
Watson is a prolific user of Twitter, recently using his feed to claim that a Sunday version of Rupert Murdoch's The Sun newspaper will launch in April.
The term 'twit-rape' is a reference to a fraudulent message left on a person's Twitter account when it is left open. The term 'frape' is also often used, referring to the same issue on Facebook.
However, the West Bromwich East MP has faced criticism today that his intern made light of rape, particularly from people unfamiliar with the 'twit-rape' context.
It has been a difficult start to the year on digital platforms for Labour, after Hackney MP Diane Abbott had to apologise for saying that ''white people love playing 'divide & rule'" on Twitter.
Last week, a Scottish Labour MP also had to resign as the party's social media tsar after he posted a joke video online portraying Scotland's First Minister Alex Salmond as Hitler.