"The health of our people and the wider public is our priority and that is where our focus is," said Arsenal managing director Vinai Venkatesham.
"We are in active dialogue with all the relevant people to manage this situation appropriately, and we look forward to getting back to training and playing as soon as medical advice allows."
Arsenal's Premier League match with Manchester City on Wednesday was postponed as a "precautionary measure" and several Gunners players went into self-isolation after Olympiakos owner Evangelos Marinakis contracted coronavirus.
Arsenal said Marinakis, 52, met a number of their players when the Gunners hosted the Greek side in a Europa League match two weeks ago.
The club said no players or staff would be tested for coronavirus.
Manchester City defender Benjamin Mendy is self-isolating as a precaution after a member of his family was admitted to hospital displaying symptoms of coronavirus.
Three Leicester City first-team players have also self-isolated after showing symptoms of coronavirus.
How things unfolded on Thursday
- 14:06 GMT - Brendan Rodgers says three Leicester City players have self-isolated after showing symptoms.
- 16:00 GMT - Manchester City's Champions League last-16 tie with Real Madrid, due to take place on Tuesday, is postponed.
- 17:25 GMT - Prime Minister Boris Johnson says the UK government is considering banning sporting fixtures - but it will not happen immediately.
- 20:45 GMT - Manchester City say defender Benjamin Mendy is self-isolating as a precaution.
- 21:30 GMT - The Premier League announces all this weekend's games "will go ahead as scheduled".
- 22:17 GMT - Arsenal say manager Mikel Arteta has tested positive for coronavirus.
- 22:33 GMT - The Premier League announces it will hold "an emergency club meeting" on Friday to discuss future fixtures.
Analysis
BBC sports editor Dan Roan
The Premier League now appears to be edging closer to an unprecedented suspension.
For several days now senior officials have privately believed matches would soon have to be played closed doors with preparations made to do so. Despite mounting criticism for carrying on as normal and being so out of step with other competitions around the world, the Premier League agreed to follow government policy.
But with several clubs now directly affected by the outbreak the integrity of the league is clearly in jeopardy. So what happens next?
Both the Premier League and EFL are desperate to get their remaining matches played.
If Euro 2020 is postponed by Uefa for a year on Tuesday, space could perhaps be created in the calendar for any delayed matches to be played, and a case could be made to government to pause the Premier League and EFL seasons for several weeks.
That would at least avert the threat of legal action from clubs claiming they have been denied promotion or European qualification. (BBC)