It is understood the West Brom midfielder, whose two international goals have come against the Welsh, sustained a hamstring injury playing against Stoke at the weekend.
The 26-year-old becomes the fourth player to pull out following the withdrawal of Ross McCormack, James Forrest and Danny Fox on Monday.
Norwich City defender Steven Whittaker was drafted in by Gordon Strachan as he prepares for his first competitive game as national team boss against the Welsh at Hampden on Friday night but there are no plans to draft in anyone else.
McCormack, who was sent home because of illness ahead of last month's friendly win over Estonia, missed Leeds' game against Huddersfield on Saturday after suffering a head knock in their previous Championship match against Peterborough.
Fox has missed Southampton's last two games after going off with a thigh injury in their defeat by QPR earlier this month.