The 32-year-old announced last May he would play his final event on home soil, and he managed one final win in the opening round in Buenos Aires on Wednesday.
But Spaniard Martinez proved too strong, and a 6-2 6-2 defeat brought the curtain down for Schwartzman, who punched above his weight during more than a decade on tour.
The Argentinian stands only 5ft 7in tall but he reached five grand slam quarter-finals, with his best run coming at the French Open in 2020, when he made the last four.
Schwartzman, whose ranking peaked at No.8 later in 2020, was honoured during an on-court ceremony.
In an essay on the ATP website, he wrote: "While it has been a little bit sad watching tennis lately knowing this moment was coming, it was in a good way.
"I have a lot of amazing memories to think about and achievements to celebrate. I had the opportunity to check off many dreams and do more than people thought was possible for me.
"I have a small body, but it gave the biggest players in our history bad moments."
Rafael Nadal was among those paying tribute, writing on social media: "Congrats @dieschwartzman on your great career! You've been a great example of fighting and overcoming and I'm glad we shared so many moments on the circuit. Enjoy your next stage!"
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