A photograph of the Labour frontbencher sipping a can of the alcoholic beverage while riding on an Overground train was published in The Sun newspaper and on its website.
Transport for London (TfL) introduced an alcohol ban on all public transport in the capital in 2008.
Ms Abbott said she was "sincerely sorry" for drinking the Marks and Spencer cocktail.
She wrote on Twitter: "A photo of me drinking from a can of M&S mojito on the Overground has been circulated.
"I'm sincerely sorry for drinking on TFL."
Ms Abbott received several supportive messages in reply to her tweet, with one Twitter user writing: "I'm sincerely sorry you feel the need to say sorry Dianne and i hope you really enjoyed the drink it's no one's business but yours."
Another said: "Put it in a water bottle next time."