The two teams had been due to play at the Amex Stadium on Saturday following the Premier League's initial decision to go ahead with this weekend's round of fixtures as planned.
Arsenal's youth team games scheduled for this weekend have also been postponed.
Less than an hour after the Premier League's statement that games would continue to be played, Arsenal confirmed that head coach Arteta had contracted coronavirus.
A statement released by Brighton read: "In light of the news that broke earlier on Thursday evening concerning Arsenal head coach Mikel Arteta and his first-team squad, we can confirm that Saturday's match against Arsenal has now been postponed.
"Arsenal confirmed on Thursday night that their head coach has tested positive for the coronavirus, and that their entire first-team squad are now self-isolating."
Brighton's chief executive Paul Barber said: "First and foremost our thoughts are with Mikel Arteta and we wish him a speedy recovery.
"It's absolutely essential the health and wellbeing of individuals takes priority and with that in mind Saturday's match has been postponed.
"We apologise to all fans for any inconvenience but trust everyone will understand that we are all facing an unprecedented situation.
"The Premier League has announced this evening that they will convene an emergency meeting of all clubs tomorrow morning, and we will update supporters on future fixtures as and when we are in a position to do so."