Robertson was taken off during Scotland's Euro 2024 qualifying defeat to Spain, with his arm wrapped in his shirt as a makeshift sling. It is thought that the 29-year-old dislocated his shoulder when goalkeeper Unai Simon landed awkwardly on him during a collision.
Liverpool are now awaiting an assessment of the damage, with Robertson's recovery timeline dependent upon whether he will require surgery or not.
Without it, the left back could return in a matter of weeks, if the damage is more severe, however, he could face months on the sidelines.
The news is a huge blow to Liverpool who face Everton at Anfield on Saturday in the season's first Merseyside derby.
Though the issue is not thought to be serious, the youngster – who was linked with Bayer Leverkusen over the summer – has returned to Liverpool for treatment and could miss a couple of weeks of action.
Kostas Tsimikas is now the only specialist left back option available to Klopp in the first-team for at least this weekend, though Joe Gomez has also played the position on several occasions for Liverpool.
Yet to make his Premier League debut, Preston-born Chambers came on as a substitute in the Reds' Carabao Cup win over Leicester and had been expected to play a bigger role in the event of Robertson's prolonged absence.
With four more Europa League games to play before the end of the year, plus the Carabao Cup clash with Bournemouth on 1 November, Chambers may well earn more opportunities once he is fully fit again.
18-year-old Calum Scanlon, who was involved in the first-team's pre-season games, could also be an option at left back in some games, while Anfield Watch writer Danny Corcoran has pitched the idea of using Jarell Quansah in the role for the weekend's Merseyside derby.