The footballer, whose identity has not been revealed, is one of the nine new or returning loan players who were present for PCR tests at the club's training base on Tuesday.
"Following PCR tests conducted this Tuesday afternoon on the group of nine players due to begin the preseason today, one of them has tested positive for COVID-19," Barca said on their website.
"The player has no symptoms, is in good health and has been quarantined at his home.
"The club has reported the matter to the relevant sporting and health authorities. All persons who have been in contact with the player have been tracked to perform the corresponding PCR tests."
Barca's first-team squad fly to Lisbon on Thursday ahead of their Champions League quarter-final against Bayern Munich the following day, but the club say this positive test will not affect their plans.
"The player has not been in contact with any of the senior team players who are scheduled to travel to Lisbon this Thursday to compete in the Champions League," they added.
Rafinha, Carles Alena, Pedri, Francisco Trincao, Oriol Busquets, Juan Miranda, Matheus Fernandes, Moussa Wague and Jean-Clair Todibo were the nine players present for tests on Tuesday.