The two sides are due to meet at the Banks’s Stadium on Saturday in the third fixture of the current League Two season.
But now Orient, who are due to play Tottenham Hotspur in the Carabao Cup tomorrow night, have had several first team players test positive.
A club statement read: “Today (Monday 21st) we received formal confirmation which shows that a number of our first-team squad have tested positive for COVID-19.
“We have informed the EFL and Tottenham Hotspur and will make a further announcement regarding Tuesday’s match shortly.
“We have also informed Mansfield Town, Plymouth Argyle and Oldham Athletic, our three most recent opponents, prior to the public release of this information.
"Leyton Orient’s priority is the health and well-being of its players and staff. Those who have tested positive will now strictly follow government self-isolation guidelines.
“The Breyer Group Stadium and training ground facilities will be closed until further notice.
“At this time, the club will make no further comment.”
Orient manager Ross Embleton confirmed after their 2-2 draw with Mansfield on Saturday that a number of his first team players missed the fixture due to 'illness' but stressed that none of them had experienced coronavirus symptoms.
Both Orient and Walsall are yet to confirm whether Saturday’s game will still take place.
Walsall have been targetting this game, or the EFL Trophy clash with Chelsea under-21s the following Tuesday, as a possible pilot match to welcome fans back.
The club enquired about the possibility of a pilot, which would see 1,000 fans return, after the EFL held seven of them at the weekend.
Now, Walsall may face the possibility of a free week following Orient’s statement.
Although the government's plan to welcome socially distanced fans back by October is still under review, the possibility of hosting a pilot on Saturday would have been a welcome relief for Walsall during an uncertain financial climate due to the pandemic.
Today's warnings from health experts about the rise of coronavirus cases could spell an end to getting fans back next month.
An EFL statement added: “The EFL has been made aware of positive test results recorded at Leyton Orient and is currently awaiting the outcome of discussions between the club and Public Health England which will determine what, if any, action is required outside of adhering to current protocols and guidance.”