The Republic of Ireland international had pulled out from the national squad at the end of May to have an abdominal operation last friday.
Ipswich's fitness coach Simon Thandani told the club website:"He will start with with general strenghtening work and if all else goes to plan and his recovery is on course, he will start running with me from about July 10th.
"Its very much down to how his recovery goes but we are hopeful he will be close to full fitness by the end of July, start of August."