The Gunners were due to participate in the Florida Cup with games against Inter on 26 July (AEST) and Everton or Millonarios on 29 July in Orlando.
Arsenal said in a statement that the "difficult decision" was based on ensuring the health and wellbeing of the club's players and staff.
Following a small number of positive COVID tests among the planned party to travel to America tomorrow, we have sadly been forced to withdraw from the Florida Cup.— Arsenal (@Arsenal) July 20, 2021
This difficult decision is based on ensuring the health and wellbeing of our players and staff.
"We fully understand what a disappointment this is for our supporters in America who were looking forward to seeing us compete in the Florida Cup as part of our pre-season build up," the statement said.
"Our apologies also go to the organisers of the Florida Cup who had done a fantastic job making the preparations and our partners who had arranged events around our participation in the competition.
"We are glad to say the members of staff are not currently displaying any COVID symptoms. They are now in self-isolation at home.
"We are now making alternative arrangements in line with the Premier League protocols to continue our preparations for the new season."
Arsenal, which drew with Rangers 2-2 and lost 2-1 to Hibernian last week in Scotland, is due to commence its Premier League season on 23 August against Brentford.
Mikel Arteta has bolstered his squad with the additions of Nuno Tavares from Benfica and Albert Sambi Lokonga from Arsenal this off-season.
David Luiz has been released while William Saliba and Matteo Guendouzi have both been loaned to Olympique Marseille.