He will be in plaster for six weeks and then face a period of intensive rehabilitation.
"Lee was reviewed by a specialist last night, and he had a scan which has revealed ligament damage in his right foot," said Ospreys physio Chris Towers.
"The problem is a fairly subtle issue, however, with the nature of the ligaments involved, there is no quick fix and to rush him back would be counter productive in the long term.
"He is essentially looking at a period of rest, in plaster, for approximately six weeks, followed by a period of rehabilitation to get him up and running and back on the field."
And in another bitter blow to both the Ospreys and Wales, lock Ian Evans has been ruled out for at least eight weeks after tearing a major tendon playing for Swansea against Pontypridd in the Principality Premiership last weekend.
"Ian Evans has suffered a tear of his pec major tendon, and having discussed the injury with a specialist, he is provisionally looking at an eight week lay-off, based on our knowledge of previous injuries of this nature," added Towers.