The setback for the 22-year-old attacking midfielder comes less than a week after he scored in the Blues' 3-0 win against Crystal Palace on the Premier League's opening weekend.
Pulisic also helped Chelsea last week lift the UEFA Super Cup, netting in the penalty shoot-out as Thomas Tuchel's Champions League winners edged out Villarreal for more silverware.
On Friday, Pulisic posted in an Instagram story: "Hi all, unfortunately I tested positive for COVID-19 earlier this week.
"Thankfully I'm fully vaccinated and I have no symptoms so far. Can't wait to get back in action! Than you for your support."
Chelsea boss Tuchel confirmed United States international Pulisic would miss the short trip to Emirates Stadium, saying: "With Christian, it's unfortunately very easy to explain.
"He had a positive test and needs to follow the protocols so he won't be available for the game."
The news follows Arsenal confirming Pierre-Emerick Aubameyang and Alexandre Lacazette were absent against Brentford last Friday after testing positive for coronavirus.
It remains to be seen whether the Gunners forwards are fit and available to face Chelsea this weekend, with Arsenal manager Mikel Arteta saying it was a "very uncertain" situation.
"They had some tough days. Laca still hasn't trained so he's not been very good," Arteta told a news conference.