The Sunderland striker believes his England team-mate will be on a high following Crystal Palace's promotion to the Premier League as the Three Lions prepare to face Italy
Zaha enters the tournament having sealed promotion to the Premier League via the playoffs with Crystal Palace and is expected to stay at parent club Manchester United next season.
The winger sat out England's first training session in Israel following their training camp in Turkey but Wickham expects him to prove a key player if he does feature in the opening match against Italy.
"He is going to be on a massive high," Wickham told the Football Association's official website. "He has done really well with what he has achieved this season, and he can only make the team stronger.
"We have strength in numbers in every position. On our day I think we can beat anybody.
"The week in Turkey prepared us physically for the weather. The vibe in the camp is good and we're looking forward to Wednesday night.
"We've had the coaching staff drum into us the importance of the tournament and I don't think anyone has any doubts in the team that we can't do well."
Liverpool midfielder Jordan Henderson, meanwhile, is confident England can deal with temperatures in Israel that have approached 40 degrees centigrade.
"It's hot, but I think we're getting used to it now," he said. "We've been out in Turkey for a week so we trained well and hopefully we can carry on to do so for the game on Wednesday.
"We're confident and positive going into the game so we'll looking forward to it and we just need to do as we have been for the last couple of the years, from the start, and I'm sure we'll be alright."