Morrison was substituted at half-time as the Baggies went down 2-0 at the Hawthorns and now seems unlikely to be available for his country's home match against Belgium on Friday night as well as the visit to Skopje four days later.
Albion manager Steve Clarke stopped short of ruling the midfielder out of the matches, but did not seem hopeful.
"He felt a pain in his groin just before half-time, the last couple of minutes in the first half," he said.
"The medical people will assess it but I would imagine he is doubtful for the Scotland trip."
Scotland lie fifth in Group A with five points from seven games.