And, earlier this week, hooker Phillips had an operation to repair a ruptured anterior cruciate ligament injury suffered in the same game.
Scarlets' head of medical Andy Walker said: "Jack underwent surgery to his shoulder on Friday morning and is expected to be out for up to 14 weeks
"Emyr underwent surgery to his knee on Wednesday and will miss the remainder of the current season.
"His rehab will begin immediately and we would expect to see him back to full fitness during the pre-season."
Condy, 21, had featured seven times from the replacements bench for the GUINNESS PRO12 leaders this season, but faces a race to be fit in time to return for Scarlets' final home game of the regular season against Glasgow Warriors on the third weekend in April.
Scarlets have lost their last two GUINNESS PRO12 encounters but bid to get back to winning ways against Connacht Rugby at Parc y Scarlets on Sunday.
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