The world No.3 converted four of six break points he earned against Altmaier and sealed the 6-3 6-2 victory in 80 minutes. He will now face Tallon Griekspoor in the quarter-finals.
Altmaier had won their last meeting in Acapulco over a year ago and Zverev admitted: "He makes it complicated."
Zverev added: "He has beaten lots of top players before. He's beaten (Jannik) Sinner, he's beaten me before, so he knows how to make it complicated.
"His shots may seem off at times, but he knows how to make it extremely complicated for the top guys, where we feel like we're not feeling the ball well."
Zverev is aiming to equal Philipp Kohlschreiber's record of three titles in Munich after he triumphed in the Bavarian city in 2017 and 2018.
Second-seeded American Ben Shelton improved after a tough first set to reach the last eight with a 7-6 (7-1) 6-3 win over Dutch lucky loser Botic van de Zandschulp.
The Australian Open semi-finalist broke early en route to a 4-1 lead but van de Zandschulp fought back to 4-4 before Shelton breezed through the first set tie-break.
Shelton broke in the opening game of the second and never looked back, wrapping up matters with another break in the ninth game on first match point after 1 hour 30 minutes.
Shelton now faces Italy's Luciano Darderi, who rallied to beat Miomir Kacmanovic, of Serbia, 2-6 7-6 (7-4) 6-4.
In Barcelona, third seed Stefanos Tsitsipas beat Sebastian Korda 7-6 (7-4) 6-4 to set up a last-eight clash with France's Arthur Fils.
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