The 50-year-old Argentine is currently asymptomatic and is self-isolating at home.
Simeone started pre-season training with his side last Monday ahead of La Liga’s start this weekend.
Atletico Madrid begin their season on September 27 at home to Granada, with their La Liga campaign delayed due to their involvement in the latter stages of the 2019/2020 UEFA Champions League last month which ended at the quarterfinal stage against RB Leipzig.
A statement from the club said: "The first team, coaching staff and auxiliary personnel underwent tests on Friday as soon as they returned from training in Los Angeles de San Rafael after a positive test was returned by a member of the travelling party in the previous tests carried out on Thursday.
"The analysis of these new samples in the laboratory has determined that our coach, Diego Pablo Simeone, has given a positive result for Covid-19.
"Fortunately, he does not present any symptoms and is isolating at his home and fulfilling the quarantine after taking training with the team since last Monday."
Simeone is the latest individual from Atletico Madrid to test positive for coronavirus after striker Diego Costa and Santiago Arias returned similar results last month.
Simeone will not be in charge of Atletico when they play Cadiz in a friendly game on Tuesday.
