The Liverpool left-back, 29, had to leave the pitch before the break in Seville with his arm cradled in his shirt after a challenge with Spain goalkeeper Unai Simon.
Robertson was replaced by Everton's Nathan Patterson.
The defender looked in discomfort as he left the pitch.
"We'll have a look and he'll go back to his club now," Scotland head coach Steve Clarke told Viaplay following the defeat in Seville.
"It always seems to happen when you lose one player in a position. We lose Kieran [Tierney] then Andy picks up a shoulder injury.
"We'll see how it is and how it settles down. Hopefully he's good for his club as soon as possible and ready to help us in November."
Scotland, who needed a draw in Seville to clinch qualification for Euro 2024, will qualify if Norway fail to win at home to Spain on Sunday.
Robertson looks likely to miss Scotland's next match against France in a friendly on Tuesday and could sit out Liverpool's derby with Everton on 21 October.
