La Liga said the players would stay at their homes where they would continue individual training before being tested again "in the next couple of days" to determine if they could return to the training ground for their club.
Many clubs, including Barcelona champions, returned to individual training as part of the second stage of the four-phase protocol of La Liga to return to activity after the pandemic stopped playing in early March.
La Liga, who said in June last week that she hoped to resume matches without spectators, said that detecting positive cases was vital to her activity return programme.
"One of those tests' aims was to detect asymptomatic cases. That way, we guarantee the safety of everyone as we return to work and comply with safety regulations in the workplace, "the statement added.
"The League has warned all participants in the training sessions not to relax the recommended safety measures at facilities or their homes to ensure that the number of infections remains low." The statement added that the League would not disclose the names of infected players as a result of data protection legislation.
Real Sociedad goalkeeper Alex Remiro said he was one of the players to test positive on Saturday.
"Many thanks for the support messages, I've tested negative on the PCR test and all I have are remains of antibodies that will soon be gone and other antibodies will soon appear telling me I'm cured," he wrote on Twitter.
"I'm going to get back to training soon but I'm going to have to keep training hard on the indoor bicycle for now."
Jhon is an incredibly talented freelance writer. He has been working of about 18 months as a reporter for some internet based print-based newspapers. He brings together significant news reports from the Technology and entertainment areas. we hope you're doing well if you see any inappropriate phrases please let us know on our contact page at the bottom. thank you! .