Having turned professional in 2010, Puig won two WTA singles titles and six ITF singles titles. On 26 September 2016, she reached her career-high singles ranking of world No. 27. On 25 May 2015, she peaked at No. 210 in the doubles rankings. She retired as a professional tennis player on 13 June 2022.
At the 2016 Rio Olympics, Puig won the gold medal, the ninth overall medal at the Games for Puerto Rico. With the feat, she also became the first Latin American champion in the women's singles discipline and is the only unseeded female player to win the gold medal since the reintroduction of tennis in 1988. During her career, Puig has defeated top-ten players Sara Errani, Caroline Garcia, Angelique Kerber, Garbiñe Muguruza, Aryna Sabalenka, and Caroline Wozniacki.