Cooper, 29, capped five times by the Tartan Army, is named in Steve Clarke's 26-man squad, but there is no place for Sheffield United's Oliver Burke while Oli McBurnie is sidelined by a metatarsal.
Blades team-mate John Fleck has been named in the party.
Sheffield Wednesday pair Liam Palmer and Callum Paterson have also missed out on a place.
Clarke has also called up the uncapped trio of Chelsea midfielder Billy Gilmour, 19, Rangers' full-back Nathan Patterson, also 19, and Celtic midfielder David Turnbull. All were regulars for the under-21s.
Former Hull City duo Andy Robertson and David Marshall was also in the squad.
Clarke's side face Czech Republic (June 14), England (June 18) and Croatia (June 22) in Group D, with the first and third games at Hampden in front of 12,000 spectators.
Meanwhile, Koch has earned a place in Germany's squad for the finals.
The squad includes a couple of surprise inclusions, including Freiburg left-back Christian Günter and AS Monaco striker Kevin Volland.
Veterans Thomas Müller and Mats Hummels have been restored to the squad after an absence of around two and a half years.
Koch is one of six players who are currently playing in the Premier League with the others being Chelsea trio Antonio Rudiger, Kai Havertz and Timo Werner, Manchester City midfielder Ilkay Gundogan and Arsenal keeper Bernd Leno.
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