Schwartzman, seeded 18 in Melbourne, lost in four sets against world no. 57 Tomas Berdych in round three.
Schwartzman broke serve to win the opening set 7-5.
Berdych of the Czech Republic hit back to level the match by winning the second set 6-3 and he went on to see out the match 7-6, 6-4 against the Argentina Davis Cup star, who is seven years younger.
Berdych's joy was shortlived, however, as he was beaten in straight sets by Rafa Nadal in the fourth round.
Camila Giorgi of Italy, ranked 27, succumbed at the same stage, against seventh seed Karolina Pliskova 4-6, 6-3, 2-6 in a marathon match lasting in two hours and 11 minutes.