The Standard's front page detailed several aspects of the Budget relating to duty changes, tax and macroeconomic figures.
It appeared on Twitter shortly before Mr Osborne stood up to deliver his Budget to the Commons.
In a statement, Evening Standard editor Sarah Sands said: "An investigation is immediately under way into how this front page was made public and the individual who tweeted the page has been suspended while this takes place. We have immediately reviewed our procedures. We are devastated that an embargo was breached and offer our heartfelt apologies."
Labour leader Ed Miliband demanded an investigation and said Mr Osborne "almost need not have bothered coming" to the Commons "because the whole Budget, including the market-sensitive fiscal forecasts, were in the Standard".
In his response to Mr Osborne in the Commons, he said: "To be fair to the Chancellor of the Exchequer, I'm sure he didn't intend the whole of the Budget to be in the Standard before he rose to his feet. I hope he will investigate and report back to the House."