The Poles, second in the group with four points, are bidding to reach the European Championship knockout stages for the first time but must cope on Tuesday without Szczesny, who damaged a thigh muscle in the opening match against Northern Ireland.
"Wojciech Szczesny is not ready for the game. All the other players are fit," Nawalka told a news conference on Monday.
Poland have not beaten Ukraine, who cannot make the last 16, in their last five meetings and lost twice to their eastern European neighbours during 2014 World Cup qualifying.
"Ukraine is a tough rival and they have individual players with high skill levels so we need to be very well prepared both emotionally and tactically," Nawalka said.
Poland have not conceded a goal in the tournament, beating Northern Ireland 1-0 before holding world champions Germany to a 0-0 draw with Lukasz Fabianski in goal.
"We are playing well, we just need to be more efficient. We have created a lot of opportunities and sooner or later I hope we will score more goals," winger Slawomir Peszko said.
Poland and Germany are level on four points at the top of the group, one ahead of Northern Ireland, but Nawalka is not concerned about looking at the permutations.
"I don't want to speculate whether we will finish top of the group or not," he said.
"We want to win every game. We will go for three points but we know how dangerous can Ukraine be. We want to show Ukraine respect by preparing properly for this game."
Peszko is certainly confident he has done all he can to get ready for the tournament.
"Since January I've sacrificed everything to be here in France. I changed my diet in general and I changed a lot to prepare myself mentally and physically," he said.
(Editing by Ian Chadband)
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