“It is something muscular. Until the doctors look at him in Barcelona we won’t know the extent of the injury,” said Barca boss Luis Enrique.
“Now we have to wait for the tests tomorrow,” Suarez posted on his official Twitter account.
“I hope it is nothing and I can be with my national team next week. Thank you for the support.”
Suarez only returned to competitive international duty in March after completing a lengthy ban for biting Italian defender Giorgio Chiellini at the 2014 World Cup.
Uruguay face Mexico in their opening match in the Copa America, which is being hosted by the United States, on June 5 before playing Venezuela and Jamaica in Group C.
Suarez scored 59 goals in a prolific season for Barcelona to become the first man in seven years other than teammate Lionel Messi and Real Madrid’s Cristiano Ronaldo to win the Pichichi prize for La Liga’s top scorer.