The school made the announcement Wednesday.
Arkansas State said it could not assemble a two-deep depth chart at one position group that would allow the game to be played safely.
"This is a result of a combination of positive tests on Monday and other players still displaying symptoms, as well as having time to safely reacclimate prior to the game," Arkansas State athletic director Terry Mohajir said in a statement.
A makeup date has not been determined.
Arkansas State previously had to move its Sept. 19 home game against Central Arkansas to Oct. 10. The school did not say if that postponement was COVID-19-related, but the program said at the time that the "health and safety of our student-athletes will always come first."
Arkansas State (1-1) is scheduled to open its Sun Belt conference slate Oct. 3 at Coastal Carolina.