The match between the Scandinavian rivals could determine who wins the group and qualifies automatically for next year's finals in South Africa. Undefeated Denmark, on 18 points, are three points ahead of second-placed Sweden with two games left.
Sweden's main problem during the campaign has been a lack of goals. They have lost 1-0 to Denmark, drawn 0-0 twice with Portugal and once with Albania, and beat Malta 1-0 last month only thanks to an own goal.
With Ibrahimovic in great form at his new club Barcelona, scoring five goals in the first five La Liga games this season, Sweden hope he will build on that momentum. He is likely to be joined upfront by Henrik Larsson, 38, who is back from injury.
Denmark, whose defence has been hit by injuries, are wary of the threat Ibrahimovic poses.
"Zlatan is one of the best right now. I have great respect for his performances," Danish striker Nicklas Bendtner told Danish tabloid BT.
"He seems to be in a fantastic form in Barcelona, but that doesn't mean he will be that for Sweden."
Sweden cannot afford to lose in Copenhagen if they want to keep alive their hopes of topping the group.
Denmark would still be in with a chance of winning the group if they draw or lose but want to win before they face dangerous Hungary next week. Sweden's opponents in the final round are the less imposing Albania at home.
"They (Denmark) are in the best position right now but we have got a big chance and now we are going to get them," daily Aftonbladet quoted Ibrahimovic as saying. "If we win, we've got a big chance of winning the group."
While Sweden have struggled to score, Denmark's troubles have been at the back because of injuries. The Danes have fielded a different defence, including a different goalkeeper, in every qualifier so far.
Liverpool defender Daniel Agger is likely to be back in the starting lineup for Denmark on Saturday after being sidelined with back problems since the Sweden match in June.
UNFINISHED BUSINESS
"It gives us a boost to have him back, and if nothing bad happens during the next training sessions, then he'll be in the lineup (on Saturday)," said Denmark coach Morten Olsen, who has some unfinished business from the last time the two sides met in Copenhagen during a Euro 2008 qualifier.
That match, in June 2007, was abandoned in the closing stages after a fan attacked referee Herbert Fandel after he awarded the visitors a penalty with the score at 3-3.
Sweden were later awarded a 3-0 victory by UEFA.
"The way I see it, we didn't lose that match. It ended 3-3," Olsen was quoted as saying by Aftonbladet.
"In my eyes, we had the upper hand during the last 20 minutes. Then things happened that we more or less could not control."
Probable teams:
Denmark: Thomas Sorensen; William Kvist, Daniel Agger, Simon Kjaer, Lars
