Cooper sustained the knee problem in the closing stages of Scotland's penultimate match before the European Championship gets underway.
Scotland boss Steve Clarke will hope the 32-year-old can recover in time for the tournament, which kicks off with his side facing hosts Germany in Munich on June 14th.
"Initial thoughts are it's just a knee-to-knee bang, so he should be fine," Clarke said.
"We'll see how he is in the morning. He's a tough man."
Cooper's injury wasn't the only worry for Clarke as Scotland laboured to kill off minnows Gibraltar at the largely-deserted Estadio Algarve in Portugal.
Clarke fielded an experimental line-up and it took second-half goals from Ryan Christie and Che Adams to spare Scotland's blushes.
"Performance-wise, the amount of chances we created in the game, it was enough to score more than two goals," Clarke said.
"The grass was really sticky. It was a different surface. It certainly wasn't a night for dribblers.
"We could tighten up a little bit with the chances we created but we got two goals, a clean sheet and we won the game so we move forward nice and positive."
The Scots host Finland on Friday in their last warm-up before heading to Germany for just their second major tournament in 26 years.
Clarke's side, who also face Hungary and Switzerland in Germany, were eliminated in the Euro 2020 group stage and are looking to progress beyond the first phase at a major tournament for the first time.
After five defeats and two draws in their previous seven fixtures, Scotland had pointed to four of those losses coming against England, France, Spain and the Netherlands.
But they hardly impressed against a Gibraltar team ranked 203rd in the world, who have now lost 13 in a row and conceded 50 goals in the process.
Clarke is pondering whether to call up a replacement for Lyndon Dykes after the QPR striker was ruled out of Euro 2024 with an ankle injury.
Yet Lawrence Shankland did little to press his case to replace Dykes at the tournament with a subdued display, while fellow forward James Forrest struggled on his first Scotland start since 2021.
Scotland finally made the breakthrough in the 58th minute as Liverpool defender Andrew Robertson crossed to the far post and Christie kept his composure to fire home from close range.
Cooper took a heavy knock on his knee and hobbled off in the closing stages. Adams came off the bench to stake his claim to be Scotland's Euro striker with a clinical finish from John McGinn's pass in the 85th minute.
