Manager Thomas Tuchel confirmed on Friday that the 22-year-old has not trained with the side since Wednesday following his positive test and will isolate for at least 10 days under government guidelines.
"Christian is unfortunately pretty easy to explain," Tuchel told reporters when asked why he wouldn't be available for Sunday.
"He had a positive test and needs to follow the protocols. He's not in training and not available for the game [against Arsenal]."
Pulisic posted on his Instagram story: "Unfortunately I tested positive for COVID-19 earlier this week. Thankfully I'm fully vaccinated and I have no symptoms so far."
The positive test comes ahead of USMNT's World Cup qualifying matches. The squad are set to meet in Nashville in nine to 10 days, with the first qualifier against El Salvador in 13 days. Sources suggest the early indications are Pulisic is aiming to be back for Chelsea's match with Liverpool next week, before he's due to join up with the national team.
Tuchel added: "I think that [a COVID resurgence] is possible, for me, my logic, my belief, but it only my personal belief that it is possible any time that this virus comes back, circulates, spreads with variations and harms society, social life and of course football, this is a possibility.
"I think that I'm not in the role to tell my players or recommend strongly to my players to get vaccinated. I am vaccinated twice. A lot of my players are vaccinated twice, Christian is also. But this is clearly the recommendation from the doctors and the medical department, they are in charge of that.
"I am not in fear but I am well aware of the risks and the situation that we still live in and we have to be careful. We have to be responsible and this is what we do here in Cobham and in everyday life. This is what we talk about with our players, of course."
Chelsea's new £97.5 million signing Romelu Lukaku is in line to make his debut against Arsenal, heightening the competition for places in the more attacking positions with Pulisic aiming to get his career back on track after a mixed 2020-21 season.
Chelsea refused to confirm exactly when Pulisic tested positive but sources told ESPN he is hopeful of being available for next Saturday's trip to Liverpool. It is not thought at this stage that any other players are affected.
Gunners boss Mikel Arteta said on Friday all four are doubtful for Sunday's game, although Lacazette returned to training on Thursday.