1,058 players and staff from England's 24 second-tier clubs had been tested for the virus on Thursday and Friday.
In a statement the EFL said 1,058 players and staff from England's 24 second-tier clubs had been tested for the virus on Thursday and Friday.
"Those players or club staff who have tested positive will now self-isolate in line with the guidelines provided by the EFL and only those who have tested negative will be permitted to enter training ground facilities," a statement read.
The EFL did not identify the individuals although Preston North End confirmed that striker Jayden Stockley had tested positive and was asymptomatic.
As well as the 10 positive tests from Championship clubs, seven positive tests were recorded from fourth tier League Two clubs.
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The news came after the latest round of Premier League tests produced no new positives.
In the three previous rounds of Premier League testing since players resumed training there were 12 positives.
Championship clubs have unanimously agreed to try to complete the season while League Two clubs are in favour of curtailing the campaign. Clubs in League One (third tier) have so far failed to reach an agreement on how to end the season.