It means he could sit out all four of Ospreys remaining league fixtures including tomorrow's (Friday) clash with Newport Gwent Dragons.
Backs coach Gruff Rees said: "We are not even putting any thought process in around when the next game for Justin can be it.
"It may be sit tight and see the season out and get to the summer."
Ospreys sit eighth in the GUINNESS PRO12 and need to overhaul an eight-point gap to Edinburgh if they're to qualify for the European Rugby Champions Cup next season.
Rees added: "We have blown so many points this year; it's an uphill task as it is. We have got to take the challenge head on.
"We cannot control everything, it's about what we put together, the aspects of going somewhere away from home and getting four tries, it has to excite our group.
"We have got to fight tooth and nail for everything for the rest of the season and see where that takes us.
"We're excited to play in a Welsh derby, we're positive about what we want to put on the park."
Welsh fans will be hoping Tipuric recovers in time for their country's three-test series against New Zealand which starts on June 11.
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