Manzambi, who has three goals and two assists at the tournament, also missed Switzerland's penalty shootout victory over Colombia in the last 16 after suffering a knee injury, and Yakin said the midfielder had failed to recover in time.
"We tried everything that we could to get him back; unfortunately, he's unable to perform tomorrow," Yakin said.
"Johan Manzambi is in a lot of pain. It was a shock to all of us. This momentum was on his side, and there is so much joy when he plays football."
Captain Granit Xhaka dismissed suggestions Switzerland, who have made the quarter-finals for the first time in 72 years, were preoccupied with eight-times Ballon d'Or winner Lionel Messi, insisting the focus was on upsetting Argentina.
Former Germany goalkeeper Jens Lehmann had raised eyebrows this week when he claimed on German television that Swiss players appeared to have "too much respect" for Messi and only wanted to leave the game with the Argentine captain's shirt.
"We cannot influence what people say about us," Xhaka told reporters on Friday. "The only thing we can do is we can perform and show what we can do on the pitch. Nothing else matters."
Yakin suggested the best way to limit Messi's influence was to deny him possession altogether. "When we have the ball, then he won't be able to act as much," he said. "We just try to play our game and not allow him to play the ball.
"There are many solutions, and we try to find the best solution. Tomorrow, on the pitch, we will perform as a unit. We will try to play good passes, press high against an Argentinian team, the reigning champions."
The 33-year-old Xhaka ranks Saturday's clash among the defining moments of his career with Switzerland, who last reached a World Cup quarter-final in 1954.
"It's going to be a highlight of my career, indeed," the Sunderland midfielder said. "Every moment when you can do something that special, it feels different.
"Now after 72 years, to be able to be here with Switzerland and to play against the reigning champions, it just makes me very proud.
"But I am not here to talk. I want to take the next steps, and we're very close to the end. I am yearning for it, I am hungry and now we just need to show how much we really want it on the pitch."
Xhaka featured in the Switzerland team that lost 1-0 to Argentina after extra time in the last-16 at the 2014 World Cup in Brazil, but he does not consider the rematch a chance to even the score.
"It's not going to be revenge. This is a completely different match," he said. "Now we are in the quarter-final, and we want to win. This is our overarching aim.
"Regarding (Swiss) fans: keep dreaming. I am a person who always dreams, and dreams can come true. If we want to fulfil our dreams, you need to work, you need to sweat, you need to push your limits if you want to beat Argentina."
The Swiss are also unconcerned about the hot conditions forecast for Kansas City, rejecting any notion that it might favour an Argentina side who have been based in the Missouri city throughout the tournament.
"When you're in the quarter-final, you don't really care about the weather," Xhaka said. "There are no excuses."
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FIFA World Cup 2026
The 2026 World Cup is taking place from June 11th to July 19th in the United States, Canada and Mexico. The tournament features 48 national teams and is played at 16 modern stadiums.
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