The 2017 Wimbledon champion, who is seeded ninth, made 33 unforced errors and hit only nine winners on No. 2 Court.
Also in the second round, eighth-seeded Jessica Pegula of the United States beat Croatian player Donna Vekic 6-3, 7-6 (2).
And 12th-seeded Jelena Ostapenko defeated Yanina Wickmayer of Belgium 6-2, 6-2. The Latvian won the 2017 French Open and was Wimbledon runner-up in 2018.
In the men's draw, top seed Novak Djokovic advanced to the third round with a 6-1, 6-4, 6-2 victory over Thanasi Kokkinakis of Australia.
The six-time Wimbledon champion has won the past three men's singles titles at the All England Club.
Casper Ruud, the runner-up to Nadal at this year's French Open, became the seventh of the top 11-ranked male players to be out of the grass-court Grand Slam for either losing early, injury, illness or being banned.
Ruud, who was seeded third but ranked sixth, lost to Ugo Humbert of France 3-6, 6-2, 7-5, 6-4 today in the second round.
The third-ranked Djokovic, No. 4 Nadal, No. 5 Stefanos Tsitsipas and No. 7 Carlos Alcaraz are the only players in the top 11 remaining in the draw. Top-ranked Daniil Medvedev is out because of a ban on Russians over the war in Ukraine, No. 2 Alexander Zverev is injured, No. 8 Andrey Rublev of Russia is also banned, No. 9 Felix Auger-Aliassime and No. 10 Hubert Hurkacz lost, and No. 11 Matteo Berrettini withdrew after testing positive for COVID-19.