McGregor started all three Scotland matches at Euro 2024 as Steve Clarke's men failed to get out of the group stage in Germany.
"I have made a decision which was very difficult, of course, but a decision which I feel is the right one at the right time," he told Celtic's website.
"Throughout my career I wanted to make myself available for Scotland at all times and whenever selected, give the absolute maximum possible to help the country and represent the supporters with passion and pride."
McGregor was also part of the Scotland side that reached Euro 2020, ending a 23-year absence from major tournaments in the process.
The news is a blow to Clarke as he begins the task of taking Scotland to a first World Cup since 1998 in two years' time.
"Callum's consistency of performance and leadership qualities have been a real catalyst in the team’s return to major tournaments," said Clarke.
"That professionalism and dedication has been a huge influence in our squad. We had a very good chat and, while I am disappointed to lose Callum’s qualities, I can understand the rationale behind his decision."
