The news was announced on Sunday by the Royal Spanish Football Federation (RFEF), which said Tuesday's planned friendly against Lithuania would now see Spain represented by the Under-21 team.
That is one of a number of measures being taken to avoid any further risks before Spain begin the upcoming tournament, with the entire squad isolating.
Spain, coached by Luis Enrique, start Euro 2020 against Sweden on 14 June in Seville.
The RFEF's statement read: "The RFEF regrets to announce that its captain Sergio Busquets has given a positive result in the last PCR test that was carried out this morning at the national team training camp in Las Rozas. The rest of the members of the camp have all tested negative.
"The federation's medical services have adopted all the necessary measures in a case of these characteristics in accordance with the protocols established by both the Ministry of Health and UEFA, so that the footballer has left the camp in a medical vehicle."
The RFEF said Busquets' colleagues and close contacts would go into isolation, with personalised training routines implemented.
Declaring the change of plans for the Lithuania friendly, which was to be Spain's final match before the European Championship begins, the RFEF confirmed the game would now "be held under the direction of Luis de la Fuente and with members of the Under-21 national team".