The 26-year-old German, who made it to the semi finals of this year's French Open, defeated Jarry in straight sets 7-5, 6-3.
Zverev will play in the semis for the third time. The German previously made it to the final of the Halle tournament in 2016 and 2017, losing to 10-time winner Roger Federer on both occasions.
Zverev will meet Kazakh Alexander Bublik in the semi finals on Saturday.
Bublik advanced earlier on Friday when Italian fourth seed Jannik Sinner withdrew hurt in the second set of their quarter final tie.
Bublik won the first set 7-5 and was up 2-0 in the second when Sinner pulled out with a right leg injury.
The Italian had taken a medical timeout at the end of the first set. He received treatment from a physiotherapist and played, and lost, two more games before pulling out.
Sinner, the 21-year-old world number nine, now faces a race against time to be fit for Wimbledon which starts in early July.
The match was the opening last-eight tie.
