Zverev, playing Tallon Griekspoor, was heckled while serving at 5-5 in the second set when the supporter yelled: "Let's go, you... wife-beater!"
Zverev did not react at first, composing himself while several other spectators jeered the heckler.
Zverev won the game, but during the changeover, he spoke to chair umpire Fergus Murphy.
"Fergus, please kick him out," Zverev said.
Organisers confirmed the spectator was removed from the stands.
"Unfortunately, there are always one or two idiots in the stadium. That is no problem," Zverev later told reporters.
Zverev was also heckled before making his runners-up speech at the Australian Open in January.
In June last year, Zverev's lawyers said he had agreed on a settlement after the mother of his child, Brenda Patea, accused him of physical abuse, and a German court closed the case.
Zverev has repeatedly denied the allegations.
He beat Griekspoor 6-7(6), 7-6(3), 6-4 in a match lasting over three hours, avenging his loss to the Dutchman at Indian Wells last month.
"I don't even care if it was a roller-coaster ride, I won," Zverev said.
"The crowd carried me to victory. I was already mentally exhausted, but they cheered me on in the decisive phase."
Zverev will face Hungary's Fabian Marozsan in the semi-finals.