These details were available from 09:00 BST but were barred from public access half an hour after the Department of Health was alerted at 16:35 BST.
MTAS has already attracted a high level of criticism and it has been reported that there are 10,000 more applicants than places available.
Jo Hilborne, chair of the junior doctors committee at the British Medical Association, told Channel 4 News: "I am absolutely appalled that it is so easy to get in and see this information which is very confidential and very personal.
"I am just flabbergasted that after we have been raising concerns about this particular system for so long now, for months, that they still have not managed to do such a basic security fix on it."
Shadow health secretary Andrew Lansley told the same programme that yesterday's breach was "shocking" and "a very serious matter".
"It is something that clearly is going to further undermine what is already desperately low morale among junior doctors, many of whom have indeed suffered considerable disadvantage to the way this system is working," he added.
Matt Jameson-Evans, spokesman for the independent doctors' group RemedyUK, said that he was "absolutely gobsmacked".
"It is a level of ineptitude that has characterised this whole process. It takes the concept of a botched IT job to a new dimension," he said.
The Department of Health apologised for the data leak and said that an investigation into the matter is underway.
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