Leishmaniasis is a widespread neglected tropical disease caused by parasites of the Leishmania genus. These parasites express the enzyme 3'-nucleotidase/nuclease (3'NT/NU), which has been described to be involved in parasite nutrition and infection. Bacteria that express nucleases escape the toxic effects of neutrophil extracellular traps (NETs). Hence, we investigated the role of 3'NT/NU in Leishmania survival of NET-mediated killing. Promastigotes of Leishmania infantum were cultured in high-phosphate (HP) or low-phosphate (LP) medium to modulate nuclease activity. We compared the survival of the two different groups of Leishmania during interaction with human neutrophils, assessing the role of neutrophil extracellular traps. As previously reported, we detected higher nuclease activity in parasites cultured in LP medium. Both LP and HP promastigotes were capable of inducing the release of neutrophil extracellular traps from human neutrophils in a dose- and time-dependent manner. LP parasites had 2.4 times more survival than HP promastigotes. NET disruption was prevented by the treatment of the parasites with ammonium tetrathiomolybdate (TTM), a 3'NT/NU inhibitor. Inhibition of 3'NT/NU by 3'-AMP, 5'-GMP, or TTM decreased promastigote survival upon interaction with neutrophils. Our results show that Leishmania infantum induces NET release and that promastigotes can escape NET-mediated killing by 3'-nucleotidase/nuclease activity, thus ascribing a new function to this enzyme.