Robertson sustained an ankle injury while representing Scotland in Tuesday's 1-0 defeat to Northern Ireland at Hampden Park.
The 30-year-old initially tried to carry on after receiving treatment in the 30th minute following a challenge by Northern Ireland defender Trai Hume.
Despite his best efforts, Robertson was ultimately forced off and replaced by Bologna's Lewis Ferguson in the 37th minute of the friendly.
Robertson's early withdrawal has left both Liverpool and Scotland sweating over his fitness, especially after the full-back sustained a dislocated shoulder while on international duty in November.
The defender had to undergo surgery to resolve the shoulder issue, forcing him to miss three months of the season before he returned to action in January.
As a result of an extended spell on the sidelines, Robertson has been restricted to 20 competitive appearances for Liverpool this season.
According to the Daily Mail, Liverpool are hopeful that Robertson's latest injury setback will prove not be a serious one.
The Reds are confident he has managed to avoid a season-ending injury, but it is still currently unclear how many matches he could miss due to the ankle issue.
The report claims they are still waiting to learn the full extent of the damage after Robertson underwent a scan on Wednesday.
Jurgen Klopp's side are set to resume their Premier League title bid with a home game against Brighton & Hove Albion on Sunday.
Liverpool will then turn their attention to a busy period, with the Reds set to play eight games during the month of April.
Curtis Jones and Ryan Gravenberch could be involved this weekend after working on their injury recoveries over the international break, while Trent Alexander-Arnold and Diogo Jota are pushing to return in the next couple of weeks.
However, Klopp is still unable to call upon the injured quartet of Alisson Becker, Joel Matip, Stefan Bajcetic and Thiago Alcantara.
Having picked up 64 points from 28 matches, Liverpool currently sit in second place and just behind leaders Arsenal on goal difference.