The central defender reportedly picked up a thigh injury in training and will return to Newcastle for medical tests later in the week.
The 29-year-old may also be a doubt as the 'Magpies' take on Brighton in the Premier League on Saturday.
Clark did not feature last Saturday as Ireland played out a goalless draw with Denmark in Dublin.
He has seen his first-team chances in the north-east under Rafa Benitez slightly limited with the arrivals of Fabian Schar and Federico Fernandez, though has still started in five of Newcastle's eight league games so far this season.