At the 2016 Summer Olympics, Puig became the first athlete to win an Olympic gold medal while representing Puerto Rico and the ninth overall medalist for that delegation. During this event, she became the first Latin American player to win the women's singles tournament. Defeating two top-ten opponents, she bested the second ranked player in the world, Angelique Kerber, in the final. Puig is the only unseeded female player to win gold since the reintroduction of tennis in 1988.

Puig started her 2016 season strongly in Sydney. As a qualifier she went on to defeat Magdaléna Rybáriková, Anna Karolína Schmiedlová, Samantha Stosur, and Belinda Bencic before losing in her second WTA final to Svetlana Kuznetsova. At the Australian Open, she reached the third round, defeating Magda Linette and Kristýna Plíšková before losing to the fourth seed Agnieszka Radwańska. In the 2016 Aegon International Eastbourne, Puig progressed as far as to the semi-finals after beating Kristina Mladenovic.
At the 2016 Olympic Games in Rio de Janeiro, Puig won the women's singles gold medal by defeating Polona Hercog, Anastasia Pavlyuchenkova, Garbiñe Muguruza, Laura Siegemund, Petra Kvitová, and finally Angelique Kerber. Puig became the second unseeded player to win a medal at the Olympics after Alicia Molik won bronze in Athens and the first athlete representing Puerto Rico to win a gold medal in any sport. Puig is the first Latin American representative to win the gold medal in singles and the second to win a medal after Gabriela Sabatini won silver at the 1988 Summer Olympics.