McMinn, who played at both clubs during his career, will be the guest of honour at Pride Park.
Derby are gearing up for the new Sky Bet Championship season and comprise a significant challenge to Rangers. The Ibrox side will hope that they are able to compete with their hosts as they prepare for a Petrofac Training Cup first round match with Hibernian on Tuesday.
Rangers have made steady progress during tours of the Highlands and North America already, although McMinn believes his former side will be worked hardest this afternoon.
"This will be the hardest test that Rangers will have faced this summer," said McMinn. "Derby are a very good side. I am sure that the Rangers players will all be looking to finish pre-season with a win ahead of their cup game against Hibs."