Clubs in the top two German divisions have returned 10 positive results from 1,724 coronavirus tests, says the German football league.
Clubs have been training in groups, with the tests taken before a planned return to training as teams.
Measures including "the isolation of the affected person" have been taken, said the DFL.
Bundesliga 2 side FC Erzgebirge Aue's entire playing and coaching staff are in quarantine at home.
One person at the club tested positive for coronavirus after the second sets of tests were carried out.
The club said the initial quarantine period was valid until Thursday after which "the entire team will have another Covid-19 smear test".
Top-flight side Cologne have had no further Covid-19 infections after three people tested positive last week and the trio are "symptom-free" but remain in quarantine for 14 days.
The Bundesliga is set to become the first major football league in Europe to return to competition.
Officials suggested resuming on 9 May but the government delayed the decision and a restart may now be on 16 or 23 May.
Cologne said in a statement that "only players who have been tested negatively twice in succession are allowed to train and play".
The DFL added: "A second wave of tests will be carried out this week - here too there may be isolated positive test results, especially since one of the tasks of this second round is to reduce the likelihood of 'false negative' findings that can never be completely ruled out."
Last week, chancellor Angela Merkel said that any decision on if and when sports activities could resume would be taken on Wednesday, 6 May.
The league has been suspended since mid-March.
The DFL has warned that many top-division teams will be in an "existence-threatening" financial position if play does not resume by June.