The 26-year-old came off the bench against Nottingham Forest on December 26 to make his first appearance since January 2014, emerging from that game unscathed after recovering from a serious Achilles problem.
He then started the FA Cup third-round tie away to Barnsley on Saturday but was stretched off two minutes into the game with an ankle issue.
It remains to be seen if Williams has suffered a recurrence of the problem that has plagued him and forced him to miss the World Cup, with Middlesbrough manager Aitor Karanka not offer a positive diagnosis after the game.
"Rhys will have a scan but it's a long term injury," he said.
"We are not sure if it's exactly the same as the last injury but it's similar and that's the worst possible thing for him.
"I just want to pass on to him my best wishes."
He then started the FA Cup third-round tie away to Barnsley on Saturday but was stretched off two minutes into the game with an ankle issue.
It remains to be seen if Williams has suffered a recurrence of the problem that has plagued him and forced him to miss the World Cup, with Middlesbrough manager Aitor Karanka not offer a positive diagnosis after the game.
"Rhys will have a scan but it's a long term injury," he said.
"We are not sure if it's exactly the same as the last injury but it's similar and that's the worst possible thing for him.
"I just want to pass on to him my best wishes."