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The Leeds captain picked up the problem in Saturday's Sky Bet Championship win over Blackburn and a scan has revealed a small tear in his groin area.
The Elland Road club said that Cooper's injury is "not thought to be major and he will work with staff at Thorp Arch with a view to being fit following the international break."
Capped twice, 28-year-old Cooper also missed the last double-header against Russia and San Marino in October with a groin issue.
Scotland boss Steve Clarke also looks almost certain to be without Scott McTominay after the Manchester United midfielder suffered an ankle injury close to the end of Sunday's 3-1 Premier League win over Brighton at Old Trafford.
Having been helped off the pitch after treatment, he was taken down the tunnel on a stretcher after several minutes of attention in the technical area.
McTominay was able to walk out of Old Trafford, albeit with a bit of a limp, and the severity of the issue will be assessed on Monday.
Michael O'Neill's move to Stoke means the Irish Football Association are on the lookout for a new manager, though the job will not be vacant until the Euro 2020 campaign has reached its conclusion.
Here, the PA news agency assesses some of those likely to be in the running.
The former Bournemouth and Luton player is well known to the IFA, having managed the under-21s and worked as an assistant to O'Neill. After a brief spell in charge of Oldham, he has impressed since taking over from Mark McGhee at Motherwell and is guaranteed to be in with a shout.
Acted as goalkeeping coach in the early days of O'Neill's tenure but left to focus on his own career as a number one with St Johnstone. He lifted the Scottish Cup in 2014 and has held down the post for over six years. Knows the terrain after a decade in international football in his playing days.
Northern Ireland's record goalscorer and key man in some of the country's most famous results, including wins over England and Spain. Already based at Windsor Park having taken over as Linfield boss in 2015, he has delivered a handful of trophies including two league titles. If overlooked for the main job, he may be groomed as next man in.
Wore the jersey with pride and passion between 2001 and 2012 and is now winning plenty of admirers at Hull, having previously coached Peterborough and Doncaster. Would be sorely tempted if approached but already has a good job in the same division O'Neill has just jumped to.
The Englishman is already on the payroll as under-21 manager, a position in which he has overseen shock victories over Spain and Iceland despite a paucity of playing resources. His knowledge of the next generation would be a plus but a homegrown candidate may be preferable. Previously assisted Robinson at Oldham, could he do so again?
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