The 19-year-old Spaniard has been one of the stories of the tournament with his run to the quarter-finals on debut at Roland Garros.
But he will not be emulating famous namesake Rafael Nadal by winning the title on debut, with second seed Zverev easing to a 7-6 (7-3) 6-1 6-3 victory.
The German's victory set up a semi-final against 20-year-old Czech Jakub Mensik, who beat Brazilian teenager Joao Fonseca 6-4 6-3 7-6 (7-3) in the late quarter-final.
In the absence of the injured Carlos Alcaraz and with both world No.1 Jannik Sinner and 24-time major winner Novak Djokovic eliminated, Zverev will surely never have a better chance to break his grand slam duck after three runner-up finishes.
However, he insisted he had already won something that mattered more to him.
Asked if he would trade the gold medal he won at the Tokyo Olympics five years ago, Zverev said: "No chance. The gold medal for me is the most difficult thing to win, because you get a chance once every four years.
"It's special in a way that there are so few people that have done it. You do it for your country, the people back home, but I wouldn't mind to add a few things to my list as well."
In the past Zverev has shown a tendency to be too passive when opportunities arise, and it appeared the same thing might be happening when he trailed Jodar 2-5 in the opening set.
But after Zverev hit back to level, it was largely one-way traffic, with the 29-year-old clinching victory after two hours and 29 minutes.
Zverev made 80 per cent of his first serves and sealed his spot in a fifth Roland Garros semi-final with a thumping forehand winner.
In the late session, Mensik won the next-generation battle against Fonseca, who had knocked out Djokovic in the third round.
But, aside from saving six match points in a remarkable game, the 19-year-old could not summon up the same magic here and instead it was 20-year-old Mensik who won 6-4 6-3 7-6 (7-3) to become the youngest Czech man to reach a grand slam semi-final.
That appeared hugely unlikely last Wednesday when Mensik lay on the clay racked with cramp after a gruelling victory over Mariano Navone, virtually collapsing into a wheelchair as the heat took its toll.
But he has rebounded brilliantly, recovering from losing the first set to love against Australia's Alex De Minaur, then coming through another five-setter against Andrey Rublev two days ago.
Mensik and Fonseca's combined 39 years made this the most youthful last-eight clash here since Rafael Nadal defeated Djokovic back in 2006.
Mensik's game is based around a precise serve that a frustrated Fonseca did not come near to breaking for two sets, while Mensik's net play was superb.
"At the end of the match there were some incredible shots and I'm super happy I'm the one who came back in the third set," said the 26th seed.
with Reuters
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