Six days before the start of the Premier League season, the left-back hobbled off after appearing to fall awkwardly and injure an ankle attempting to stop a cross.
Robertson was helped off the pitch by the club’s medical team shortly before half-time in the 1-1 draw.
Scotland have three crucial World Cup qualifiers in eight days next month. Steve Clarke’s men are away to Denmark on September 1, home to Moldova on September 4 and away to Austria on September 8.
Liverpool manager Jurgen Klopp said: “We don’t know how serious it is. It was pretty painful and that is why Andy went off.
“He got the ball on the front of his foot, twisted his ankle. The pain settled already but we cannot say without further assessment.
“He needs to get a scan and then we will know more.”
