The 27-year-old was stretchered off in the early stages of the game at Portman Road on April 9 after a hefty challenge from Ipswich's Luke Hyam and is expected to miss a number of months.
A statement issued by Brentford after the game confirmed that Judge's lower leg was fractured and that the player and his family would receive the club's "fullest support" during this difficult time.
"The injury was assessed and immobilised locally and Alan has now been transferred to a London hospital where he will managed by the leading lower limb consultant in the country," the statement read.
"The nature of his management and long-term prognosis cannot be speculated on at this time, however it should be stated that a full recovery is not in question.
"Alan and his family will receive our fullest support and further comment will be provided as we're able to over the coming days."
The injury comes as a serious blow to Judge, who had recently made his senior Ireland debut against Switzerland in March and was aiming to force his way into Martin O'Neill's plans for Euro 2016.