The 30-year-old former Rangers stopper, who joined Turkish side Besiktas on a free transfer in July, was substituted after 23 minutes of Scotland's 3-1 friendly win over Australia last month with a groin strain.
"He played on Saturday and kept a clean sheet," said Houston. "We are absolutely delighted he's fully fit because his experience in playing big international matches is vital.
"We were convinced after the Australia game that he was struggling. He had a couple of injections and recovered brilliantly. Fair play [to Besiktas] for getting it sorted."
McGregor has been capped 22 times at senior international level.