The 7-6(5) 1-6 4-6 6-3 7-5 defeat means former world number three Tsitsipas will end the season without playing in the third round of a Grand Slam for the first time since 2017.
Altmaier deployed the legal but rarely used underarm serve a few times as he rallied in the fourth set and Tsitsipas let the German know he did not approve as the pair shook hands at the end of a contest that lasted four hours and 26 minutes.
"Next time, don't wonder why I hit you, okay? No, I'm just saying if you serve underarm ... if you serve underarm," Tsitsipas told Altmaier, implying he had targeted the German's body during the contest.
The crowd booed as the German world number 56 backed away with his hand raised refusing to engage in the discussion.
Tsitsipas, a former finalist at both the Australian and French Opens, parted ways with his coach Goran Ivanisevic and brought his father Apostolos back on board last month in an attempt to arrest a worrying decline in his game.
The 27-year-old has not won back-to-back matches since the Barcelona Open in April and has sunk to 28th in the world rankings.