Robertson was caught by Northern Ireland's Trai Hume in the 30th minute of the contest, which led to him receiving treatment, but the defender was initially able to continue.
The 30-year-old did not complete the first half, though, exiting the field in the 37th minute, with Lewis Ferguson his replacement in the contest at Hampden Park.
Robertson appeared concerned when he left the field, and his injury will now be assessed by both Scotland and Liverpool before the best course of treatment is determined.
The injury will almost certainly rule him out of Liverpool's next match, which is a home fixture against Brighton & Hove Albion in the Premier League on Sunday afternoon.
Liverpool will then face Sheffield United and Manchester United in back-to-back Premier League matches before welcoming Atalanta BC to Anfield for the first leg of their Europa League quarter-final.
Robertson has been restricted to just 20 appearances for Liverpool this season, having missed a chunk of action due to a shoulder injury.
The Scot made his return at the end of January, but his fitness has been managed since then, only completing the full 90 minutes in two of Liverpool's last seven league games.
Robertson was a second-half substitute in Liverpool's 1-1 draw with Manchester City in the team's last league match, but he then started against both Sparta Prague and Man United.
Scotland boss Steve Clarke is expected to provide an update on Robertson's fitness after the clash with Northern Ireland, although the full-back will need to undergo a scan to determine the extent of the damage.
Injuries have been a problem for Liverpool throughout the season, but Jurgen Klopp's side are still competing on two fronts, while they won the EFL Cup last month.
Joel Matip, Alisson Becker, Stefan Bajcetic, Trent Alexander-Arnold, Diogo Jota, Curtis Jones, Ibrahima Kone, Darwin Nunez and Thiago Alcantara are all currently in the Liverpool treatment room.