The Vogue hitmaker was performing at The Wiltern when she spotted the "Panini" hitmaker in the front row and stepped down from the stage to share an intimate exchange with the star.
"That looks so thirst-quenching, may I have a sip," she asked, pointing to his beer. "If I drink this, I'll be getting some of your backwash."
The singer added, "Kinda sharp, your backwash. Might cut my tongue."
Nas, real name Montero Lamar Hill, seemed totally at ease, however, as he gushed, "I'm in the presence of a legend, I'm just happy to be here."
After breaking the ice, the pair thrilled the crowd as they casually chatted, with Madonna telling the rising star she'd been to his hometown of Atlanta, Georgia "like three billion times."
She then asked Nas if he actually rode a horse, in reference to his summer smash "Old Town Road", quipping, "I'll teach you how to ride, baby," before leading a round of the hit tune with the audience.
While phones and cameras are not allowed at Madonna's Madame X shows, an official recording of the encounter was shared on the "Hung Up" singer's Instagram page.