The 22-year-old, who had never won a match in the main draw at a Grand Slam competition before arriving in Paris, won 6-2, 7-6, 6-4.
Altmaier, ranked at 186 in the world beat the Spanish veteran Feliciano Lopez in the first round and then he saw off his fellow German Jan-Lennard Struff in the second round.
He beat the 30th seed 6-3, 7-6, 6-3.
In the first match before a spattering of fans on Courth Philippe Chatrier he was aided by a host of Berrettini errors to progress in two hours and 20 minutes.
“It’s my first time in Paris and it means a lot to me,” he told on-court interviewer Fabrice Santoro.
“My coach and I have been working hard to be here. I have been struggling with injuries so I’m happy to be in the fourth round.”
There was also a straight sets win for the 13th seed Andrey Rublev. The 13th seed overwhelmed the South African veteran Kevin Anderson 6-3, 6-2, 6-3 to reach the last 16 for the first time.
