The Serie A leaders, eliminated from the UEFA Champions League after finishing third in Group B behind Real Madrid and Galatasaray, will start their campaign to win the Europa League for a record fourth time against the Turkish club.
Trabzonspor qualified for the last 32 by finishing above Lazio at the top of Group J, and have yet to taste defeat in this season's competition.
And former Juve midfielder Nedved is far from pleased with the tie, which he believes will be tough for Antonio Conte's side to negotiate.
"I'm not that happy about having to go to Turkey again," Nedved told TuttoMercatoWeb.
"Things haven't gone too well for us there in the recent past.
"It will be a tough and long away trip. We will have to find the right motivation to play it as Juventus."
Juve could face Serie A rivals Fiorentina in the last 16 should they overcome Mustafa Resit Akcay's side, but Nedved is not looking past Trabzonspor.
"Fiorentina? Let us just think about one game at a time," he added.
"The Europa League is not a competition that you should underestimate, there are good sides who are tough to take on.
"We have to take it step by step."
Trabzonspor drew twice with Lazio in the group stage and won at Inter in 2011-12 UEFA Champions League.
And president Ibrahim Haciosmanoglu is confident Akcay's team can progress past the Italian champions.
"Juventus were knocked out of the Champions League by a Turkish side and we can give them the pleasure of being eliminated by another," Haciosmanoglu said.
"It's an advantage to play the first match at away. If we get a positive result there, we believe we can clinch the tie in Trabzon."
