The left-back rolled his ankle when attempting to block a cross against Athletic Bilbao in a pre-season friendly at Anfield.
He was able to walk off the pitch, with the help of club medics, and will undergo a scan on Monday to determine the extent of the damage.
“We don’t know in this moment how serious it is,” said Jurgen Klopp said after the game.
“He twisted his ankle. The pain settled already but further assessments tomorrow with a scan. Then we will know more.”
News of a possible setback for Robertson is a huge blow just six days before their first game of the season, away at Norwich City.
There was better news for Virgil van Dijk, who played 72 minutes as he continues his return to action.
Liverpool face Osasuna in their final pre-season friendly on Monday.