Second row Evans was injured playing for Swansea in against Ponytpridd in the Welsh Premiership on Saturday evening, while Byrne was forced off during the Ospreys 32-32 draw with Leicester the following day.
Towers commented:
"Lee was reviewed by a specialist last night, and he had a scan which has revealed ligament damage in his right foot.
"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.
"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."
Ospreys medical updates are sponsored by Vale Healthcare
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland