The winger played the full 90 minutes for Newcastle against Liverpool but the Scottish Football Association announced on Sunday evening that he had pulled out of the squad.
There are currently no plans to call up a replacement.
Ritchie joins Celtic duo Stuart Armstrong and Scott Brown, who have also been ruled out of the two qualifiers that will determine Scotland's fate.
Lukaku completes loan move back to Inter from Chelsea
The withdrawals of Armstrong and Brown prompted Scotland boss Gordon Strachan to call up Celtic midfielder Callum McGregor earlier on Sunday.
The 24-year-old took his goals tally for the season to six with a double in Celtic's 2-2 draw against Hibernian on Saturday.
The uncapped McGregor has only been called up once previously, for a European Championship qualifier against Germany in 2014, but his recent form had led to calls for him to be included again.
Armstrong's withdrawal had left Strachan short of options in the advanced central midfield role. James Morrison was an unused substitute in West Brom's 2-2 draw with Watford on Saturday and has not been a regular starter this season, although he played the second half of Scotland's 2-0 victory over Malta in their previous qualifier.
Hibs midfielder John McGinn gave a reminder of his goalscoring prowess as he also hit a double at Parkhead on Saturday.
Scotland's squad were meeting up on Sunday despite a number of players still being on club duty, and Strachan will desperately hope Ritchie is the only casualty.
Ramos asked Rubiales to help win Ballon d'Or in 2019 - report
Raphinha's Chelsea move hits hurdle as agent Deco tries to force Barcelona move