The Danes picked up a surprise point against Juventus two weeks ago, but Carlo Ancelotti's men will be desperate to avoid two home losses in a row.
The Danish outfit has never defeated a Spanish opponent in eight attempts, but the club will be buoyed by the 1-1 home draw earned against Juventus on matchday one.
Real was in imperious form in its opening Group B fixture, Cristiano Ronaldo scoring a hat trick in a 6-1 demolition of Galatasaray in Turkey.
The two sides have never met before, with Real's last game against a Danish side ending in a surprise 2-0 home reverse to Odense in what was then the UEFA Cup in 1994-95.
The last time Copenhagen came up against a side from La Liga was three years ago when it took a point from two games against Barcelona in the Champions League group stages.
That season the club went on to deliver the best performance by a Danish side in the competition, reaching the second round before being eliminated by Chelsea.
The Blancos exited at the semifinal stage of this competition for the third year in succession last season, while Copenhagen was edged out 2-1 on aggregate by Lille in the final qualifying round.
Carlo Ancelotti's side suffered its first league defeat of the season on Saturday, going down 1-0 at home to neighbor Atletico, a result that leaves the club five points adrift of both Diego Simeone's men and Barcelona at the top of the table.
World-record signing Gareth Bale is in line to feature, the Wales international coming off the bench during the weekend defeat after recovering from a thigh injury, but midfielder Xabi Alonso remains sidelined with a broken foot.
Copenhagen has suffered a terrible start to its domestic campaign and with just two wins from the opening 10 matches, Stale Solbakken's side currently finds itself in the relegation zone, the club's plight not helped by Saturday’s 3-2 defeat away at Brondby.
That reverse was Solbakken's first defeat since taking over from Ariel Jacobs in August and Copenhagen will be hoping to celebrate its 150th European game with what would be a surprise win.