The 21-year-old Denmark defender landed awkwardly after a collision with Peter Madsen in Sunday's match away to Lyngby.
A subsequent scan has uncovered ligament damage in Zanka's left knee, setting him up for a prolonged period on the sidelines.
As his team-mates take to the pitch Thursday night, Zanka will be recovering from surgery scheduled for earlier in the day.
Zanka was philosophical about the news, admitting it was a blow but adding that he was relieved it was not more serious.
"Obviously I am disappointed to have a long period of recovery ahead of me and I will miss a lot of exciting games this autumn," he told the club's website.
"Conversely however, I am glad that it is the best-case scenario: that it is only ligament damage. I will have surgery on Thursday, where there will be an investigation into how complicated the injury actually is. I am therefore optimistic despite the disappointment."
Copenhagen go into the game on the back of a 1-0 away win over Lyngby that puts them seven points clear at the top of the Superliga standings.
That domestic form compares very favourably with that of their opponents, who beat Chernomorets 3-1 at the weekend but remain down in sixth place, already nine points adrift of Shakhtar Donetsk after nine matches.
However, Vorskla can point to a seven-game unbeaten run in Europe as they came through the qualifiers to reach this stage.
But Nikolai Pavlov's team have injury problems of their own, with the coach confirming that both Jovan Markoski and Serhiy Zakarlyuka will be missing for the game.
Markovski recently sustained a fractured finger, but the Serbian has also suffered a family bereavement and he will not be included in Thursday night's plans.
Zakarlyuka has recently been suffering from spasms and will not be risked.
"We have young players who we will trust in their place, not least because we have no choice," said Pavlo