Greek second seed Tsitsipas, who triumphed at the Monte Carlo Country Club in the last two editions, was never in the mix against Fritz, who reached the last four of a Masters event for the first time.
Eighth-seeded Fritz raced to a 4-0 lead in the opening set, which he wrapped by winning his service game to love.
Tsitsipas improved slightly in the second set, only for Fritz to break decisively for 4-3 with a winner.
He then held firm to set up a semifinal meeting with Russian Andrey Rublev, who earlier overcame some second-set nerves to dispatch German qualifier Jan-Lennard Struff with a 6-1, 7-6(5) victory.
Rublev lost the first game on his serve before bagging six in a row in a quick opening set, but Struff, the world No 100, found his stride in the second as the fifth seed showed signs of nerves.
Rublev broke for 4-3, only for Struff to break back in the following game and force a tiebreak, in which the Russian regained his composure to prevail on his second match point.
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