The Dragons second row is set to return in April after undergoing surgery on the injury sustained during Wales' Autumn Nations clash with Argentina last month.
Rowlands unavailability is a huge loss for his nation, which begins its campaign against Ireland in early February before concluding against France six weeks later.
A string of impressive performances in 2022 saw the 31-year-old named player of the year by the Welsh Rugby Writers Association (WRWA).
"The shoulder is OK. It is frustrating, but [the recovery] is just slow and steady," he told the Scrum V Live program.
"Hopefully I will be involved back in rugby in April."
Rowlands, who is reportedly set to join French side Racing 92 after leaving the Dragons at the end of this season, is also doubtful for the World Cup in September due to not fulfilling the Welsh Rugby Union (WRU) selection criteria.
The policy states players playing their domestic club rugby outside Wales must have earned 60 or more caps to remain eligible for selection, thus rendering the 23-cap lock unavailable to Warren Gatland.
