Derry playmaker was also named League of Ireland player of the month and takes his place in squad for friendly on Friday, May 31
McNamee is the only domestic-based and uncapped member of the 16-strong group and was earlier named as the League of Ireland's Player of the Month for April.
Ireland manager Noel King has also invited five other League of Ireland players, as well as Selcuk Tidim from Hansa Rostock II, for training ahead of the Denmark clash, which functions as a warm-up opportunity ahead of the Uefa Euro 2015 qualification campaign. Ireland kick-off their Euro journey on August 14 with a match against the Faroe Islands in Torshavn.
King said: "This is our last preparation game before our first Euro 2015 qualifier against the Faroe Islands in August, so it's obviously our final chance to see players before then. Some players are missing through injury, suspensions etc, but this could be the case in August also, so we'll prepare with that in mind.
"Denmark are terrific opposition for us for this game. They are a strong side, but we'd prefer to face a powerful team in order to prepare for the important qualifiers we have in August."
Ireland U21 will meet in Dublin on May 26 and travel on May 29 to play Denmark at the Fredericia Stadium, Fredericia, at 16:00 CET on Friday, May 31.
Aaron McCarey (Wolverhampton Wanderers), Sean McDermott (Sandnes Ulf), Shane Duffy (Everton), Anthony O'Connor (Blackburn Rovers), Matt Doherty (Wolverhampton Wanderers), Joel Shaughnessy (Aberdeen), Derrick Williams (Aston Villa), Sean McGinty (unattached), Carl McHugh (Bradford City), Samir Carruthers (Aston Villa), John O'Sullivan (Blackburn Rovers), Frankie Sutherland (QPR), Barry McNamee (Derry City), Sean Murray (Watford), Anthony Forde (Wolverhampton Wanderers), Aiden O'Brien (Millwall)
Training: May 26-29
Daryl Horgan (Cork City), Roberto Lopes (Bohemians), David O'Leary (Limerick), Ciaran Gallagher (Finn Harps), Danny Morrissey (Cork City), Selcuk Tidim (Hansa Rostock II)