The 32-year-old has already had the bone relocated and will undergo an operation next week but his Six Nations chances are effectively over.
Kidney was already seeking reinforcements after Rob Kearney's chances of making the opening games against Italy and France were put in doubt by a knee injury.
And Murphy, who was initially thought just to have damaged his ankle ligaments, admits the blow couldn't have come at a more inopportune moment.
"Effectively, my chances of playing in the Six Nations this year are gone," he said.
"It's very frustrating really. It's the nature of the game, though, nothing can be done. You have to just get on with it, really.
"It's very annoying. I just have to try and get back as quickly as possible."
Kearney injured his knee in the autumn defeat to New Zealand and winger Luke Fitzgerald is now tipped to fill in at 15.
Ireland's hopes of regaining the Six Nations crown were dented even further with the news that hooker Jerry Flannery is also set to miss the start of the championship with a torn calf muscle.