Neil Lennon's men were pitted against the Danes who finished second in their group behind Malmo.
The 13-time Danish champions won the league last season but, like Celtic, were knocked out at the Champions League qualifying stage.
There will be a familiar face for Celtic fans in Nicklas Bendtner who was part of the Rosenborg side they faced regularly.
Copenhagen are currently second in the Danish Superliga. They trail Erik Sviatchenko's FC Midtjylland by seven points, albeit with a game in hand.
It will be the club's first meeting with Copenhagen since the 2006/2007 Champions League group stage. Both sides won their home fixture as Celtic finished runners-up behind Manchester United.
The league leaders created history by becoming the first Scottish team to qualify from a European group stage with two games to spare having beaten Lazio home and away.
The first-leg will take place on Thursday, 20 February. The return leg is scheduled for the following week.