Thomas aggravated the groin injury during the Ospreys' Heineken Cup defeat to Perpignan on January 17 and has since had an injection to try and ease the problem.
"Jonathan is very unlikely to play, he hasn't taken much of a role in training," said Wales coach Warren Gatland.
"He had an injection and the groin has come out alright."
The 26-year-old missed all four of the November internationals against South Africa, Canada, New Zealand and Australia due to a long-standing groin injury but the reason for his expected absence this time around is thought to be less serious.
Thomas, who currently has 46 international caps to his name, was part of his country's Grand Slam-winning seasons in 2005 and 2008 and had been in line to earn his place in the matchday 22 when Wales travel to Edinburgh this weekend.