The hosts edged out Paris FC in their opening group game, while the Spanish side held Chelsea to a 2-2 draw in Madrid.
Match preview
After losing in qualifying last season, Hacken are back in the Champions League group stage following a 4-3 aggregate victory over Twente in the playoff round.
Hacken, who are competing in the main draw for the second time in three seasons, have been given a tough group featuring Chelsea, Real Madrid and Paris FC.
The Swedish side began the group stage with an away trip to Paris, where they were looking for a response after missing out on the Damallsvenskan title on goal difference.
Fortunately, Mak Lind's side picked themselves up from that disappointment to claim a 2-1 victory thanks to goals from Rosa Kafaji and Anna Sandberg.
With their domestic campaign completed, Hacken have had a week to prepare for Thursday's clash, where they will look to extend their unbeaten home run to 14 games across all competitions.
Real Madrid are competing in the main draw for a third consecutive season after they eased to a 5-1 aggregate victory over Valerenga in qualifying.
Las Blancas were given a much tougher test in their opening group game against Chelsea, which produced a controversial 2-2 draw.
Olga Carmona opened the scoring before goals from Niamh Charles and Sam Kerr turned the game in Chelsea's favour, but Spain's World Cup hero was given the chance to restore parity and score her second goal of the game following the award of a controversial penalty.
Carmona kept her composure to dispatch the spot-kick, and there was to be more drama in stoppage time when the Women's Super League champions had a goal harshly ruled out for offside, ensuring Las Blancas picked up a precious point in their opening group match.
Although they would have been pleased with last week's draw, Alberto Toril's side will travel to Sweden in a despondent mood after they were thrashed 5-0 by bitter rivals Barcelona in Sunday's Clasico.
BK Hacken Women Women's Champions League form:
D
W
W
BK Hacken Women form (all competitions):
Real Madrid Femenino Women's Champions League form:
W
W
D
Real Madrid Femenino form (all competitions):
Advert - content below:
Team News
The hosts are unable to call upon long-term absentees Anna Csiki and Stine Larsen, who is recovering from an anterior cruciate ligament injury.
Clarissa Larisey remains unavailable with a foot problem, and she is joined on the sidelines by Elin Rubensson.
Midfielder Hanna Wijk is also a doubt for the hosts after she missed last week's victory over Paris FC due to illness.
As for the visitors, Colombia international Linda Caicedo has been ruled out until January after injuring her ankle ligaments in the Clasico.
Sandie Toletti and Naomie Feller have also been added to an injury list that includes long-term absentees Caroline Weir and Carla Camacho.
After featuring as substitutes at the weekend, midfielders Claudia Zornoza and Maite Oroz are set to come into the side for Thursday's away trip.
BK Hacken Women possible starting lineup:
Falk; Kosola, Rybrink, Luik, Nelhage; Bergman-Lundin, Curmark; Anvegard, Rosa, Sandberg; Masaka
Real Madrid Femenino possible starting lineup:
Misa; Hernandez, Ivana, Kathellen, Carmona; Oroz, Abelleira; Raso, Zornoza, Del Castillo; Bruun
We say: BK Hacken Women 1-2 Real Madrid Femenino
Although Real Madrid would have been disappointed with Sunday's league defeat to Barcelona, they do boast a decent record in the Champions League, having lost just two of their last 13 matches in the competition (W4, D3).