The match was underway when it came to light that the player, who did not travel with the squad to Bristol, had tested positive and other members of the squad had been in contact with him in the last 48 hours.
"The match officials, following agreement from both participating clubs, called off the match as a precaution due to a Covid-19 related issue," the ECB said in a statement.
Gloucestershire were 66-6 at lunch when the match was abandoned.
Northamptonshire have fielded a multitude of white-ball specialists in the T20 Blast of late, with only two of their XI for the first-class fixture against Glamorgan having featured in their most recent Blast game, a three-wicket win over Glamorgan on Thursday.
While England, along with the West Indies, Pakistan and Australia tourning parties this summer, have been asked to stay in biosecure "bubbles", county cricketers have been asked to sign up to a code of conduct and have regular temperature checks and health questionnaires.
The ECB will now assess with whom the player in question has been in close contact with before deciding on next steps, but there are fears that he could have infected team-mates and opponents alike.