Robertson was forced off late in the first half of the Euro 2024 qualifier following a challenge from the Spain goalkeeper Unai Simon.
The left back appeared to have suffered a dislocation and left the pitch with his arm wrapped in his shirt, which he was using as a makeshift sling.
Scotland went on to lose their first match of their Euro 2024 qualifying campaign, following Scott McTominay’s controversially disallowed goal.
It means Scotland could be forced to go to Georgia in November needing a result, unless Norway fail to beat Spain in Oslo on Sunday.
Robertson could be missing for the fixture but the more immediate concern is upcoming games for Liverpool, with the Merseyside derby against Everton a week on Saturday on October 21.
Scotland manager Steve Clarke has already ruled Robertson out of Tuesday’s friendly against France and said the defender will now undergo a scan back at Liverpool.
"It was an immediate decision to take him off, he’ll go back to his club, he’ll be assessed," Clarke said.
"Obviously he’s hurt his shoulder. We’ll have a look, obviously go back to his club. Always seems to happens when you lose one player in a position: we lose Kieran (Tierney) on the left side and then Andy’s picked up a shoulder injury.
"We’ll see how it is, see how it settles down and hopefully he’s good for his club as quickly as possible and he’s ready to help us in November."
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