Details of the Budget are supposed to be kept under wraps until the chancellor announces them in the House of Commons, due to them being market-sensitive.
But early publication of the OBR's report effectively confirmed a number of new measures, including a pay-per-mile charge on electric vehicles, and a three-year freeze on income tax and National Insurance thresholds.
The OBR quickly removed the forecast document from its website and apologised for the release, which it blamed on a "technical error".
Speaking to BBC Radio 4's Today programme on Thursday, Mr Hughes said the document was not published "on our web page itself".
In other words, it was not linked to directly by the OBR website.
However, it had still been published online ahead of the Budget being announced.
"It appears there was a link that someone was able to access," he said. "We need to get to the bottom of what exactly happened."
Mr Hughes said Professor Ciaran Martin, a former head of the National Cyber Security Centre, would provide "expert input" for the OBR's investigation.
The BBC was able to access the PDF version of the OBR's key report at 11:45 on Wednesday by replacing the word 'March' with 'November' in the web address of a previous edition.
Five minutes earlier, the Reuters news agency had started sending out one-line news flashes summarising contents of the report.
This was followed by a brief spell of volatility in the UK bond and currency markets.
Gilt yields - which give an indication of government borrowing costs - fell sharply, before climbing back to above the level they had been at before the details were leaked.
Although this is the first time the OBR has made this sort of mistake, it is not the first time parts of the Budget have leaked out before they should have done.
Back in 2013, the Evening Standard mistakenly published details of George Osborne's Budget before he got to his feet in the Commons, including details of major announcements on tax.
The then-Labour leader Ed Miliband was reading a photocopy of the front page as Osborne spoke and said the chancellor "almost need not have bothered coming" to the Commons.
In 1996, the Daily Mirror was sent the full contents of Chancellor Ken Clarke's Budget in advance of his speech.
Piers Morgan, who was the paper's editor at the time, only published some details in the next day's paper, sending the rest back to the Treasury.
At the time, prime minister John Major ordered a leak inquiry and the Metropolitan Police investigated, but no one was arrested.
In 1947, the Labour Chancellor Hugh Dalton was forced to resign after giving a journalist details of the Budget before making his statement.