The former UN climate chief led 195 countries to agree an historic pact to tackle global warming in Paris last December, and hoped this success would convince governments to back her in the contest for the New York post.
But a series of straw polls among the UN Security Council saw Figures finish close to bottom, receiving support from just two countries.
In a letter the Costa Rican said she was pulling out through "loyalty to the United Nations and in order to facilitate the advance of the selection process."
Figures added there was still a need for a "new era" of multilateralism to tackle a variety of interconnected issues such as conflict prevention, human rights, migration and climate change.
"Never before have we had so many issues compounding each other," she added.