The Ibrox club said, after consultation with police, two fixtures would be moved.
Rangers' Scottish Challenge Cup First Round game on July 26 and Scottish League Cup First Round on August 2 will be moved to new dates.
The new fixture dates will be announced in due course.
A statement from Rangers said: "Following consultation with Police Scotland and as a result of the Commonwealth Games - Glasgow 2014 - taking place at the same time, the SPFL will reschedule Rangers fixtures planned for Saturday July 26 (Scottish Challenge Cup First Round) and Saturday August 2 (Scottish League Cup First Round) to alternative dates.
"An announcement on the new dates for these two fixtures will be made in due course."
Rangers will now meet Derby County in a friendly on August 2 at the iPro Stadium.
The Rams, managed by former England boss Steve McClaren, will host the Light Blues a week before the SPFL Championship begins.
McCoist’s side also play pre-season games against Buckie Thistle and Brora Rangers before heading to America and Canada to meet Ventura County Fusion, Sacramento Republic FC, Victoria Highlanders and Ottawa Fury FC in July.
McCoist, speaking on the club website, said: “Derby were very unlucky not to clinch promotion so they will certainly give our boys a tough test.
“Our squad will have featured in six pre-season friendlies before we meet Derby and this match will help us prepare for our Championship campaign.”