The Ospreys have revealed that Beck is unlikely to play again before the end of February due to an ankle ligament problem.
Although Jonathan Davies and Jamie Roberts are expected to form Wales' midfield pairing for the Six Nations opener against Ireland on February 2, Beck has established himself as a key squad member.
The 22-year-old was injured during Ospreys' RaboDirect PRO12 game against Newport Gwent Dragons on New Year's Eve.
"Ashley suffered a significant ligament injury to his ankle during the New Year's Eve fixture at Rodney Parade," said Ospreys head physiotherapist Chris Towers.
"We have conducted investigations over the course of the last week to determine the full extent of the ligament damage and plan his rehabilitation effectively.
"Based on the advice received, we are currently treating this as a six-eight week injury so would expect to see him back in action by the end of February."
Wales' interim head coach Rob Howley, in charge for the Six Nations while Warren Gatland concentrates on British and Irish Lions business, has already lost fly-half Rhys Priestland (Achilles tendon), lock Luke Charteris (knee) and prop Aaron Jarvis (knee) from his plans due to injuries.
Ospreys second-row forward Alun-Wyn Jones, meanwhile, is currently recovering after shoulder surgery, and flanker Dan Lydiate has not yet played since suffering a serious ankle injury earlier this season.
Jones and Lydiate are both given chances of featuring at some stage of the Six Nations campaign, but there are plenty of areas for Howley to ponder before his scheduled squad announcement next week.
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