Victory over Wales clinched second spot in qualifying Group D but Meyler was booked in that match to earn his suspension.
James McCarthy, who played his first football of the season in Everton’s 2-1 Carabao Cup defeat at Chelsea on Wednesday evening after finally shaking off the knee injury he sustained in pre-season, has also been named in an initial 34-man party for the two-legged play-off.
McCarthy’s fitness or otherwise was the source of tension between international chief Martin O’Neill and club manager Ronald Koeman, who was sacked earlier this week.
Ireland head for Copenhagen on Saturday, November 11 with the return taking place at the Aviva Stadium three days later.
The squad includes goalkeepers Darren Rudolph (Middlesbrough), Keiren Westwood (Sheffield Wednesday) and Colin Doyle (Bradford City).
Republic of Ireland squad: Darren Randolph (Middlesbrough), Keiren Westwood (Sheffield Wednesday), Rob Elliot (Newcastle), Colin Doyle (Bradford); Cyrus Christie (Middlesbrough), Matt Doherty (Wolves), Paul McShane (Reading), Richard Keogh (Derby), Shane Duffy (Brighton), Ciaran Clark (Newcastle), John O’Shea (Sunderland), Kevin Long, Stephen Ward (both Burnley); Aiden McGeady (Sunderland), Daryl Horgan, Alan Browne (both Preston), Glenn Whelan, Conor Hourihane (both Aston Villa), Harry Arter (Bournemouth), James McCarthy (Everton), Robbie Brady, Jeff Hendrick (both Burnley), Eunan O’Kane (Leeds), David Meyler (Hull), Wes Hoolahan (Norwich), Callum O’Dowda (Bristol City), Jonny Hayes (Celtic), James McClean (West Brom); Shane Long (Southampton), Daryl Murphy (Nottingham Forest), David McGoldrick (Ipswich), Sean Maguire (Preston), Scott Hogan (Aston Villa), Aiden O’Brien (Millwall).