The game is the second League Cup group match to be called off after Ross County were forced to pull out of their trip to Forfar Athletic, with the Loons awarded a 3-0 victory.
The Staggies also suffered an outbreak of Covid-19 with a number of players and staff affected, leaving them unable to fulfil their opening fixture.
A league statement read: "Dumbarton informed the SPFL that a player had tested positive for Covid-19 and, as a result of close contacts and player injuries, they do not have sufficient players available to fulfil the fixture."
A statement from the League One side read: “Dumbarton FC can confirm that a positive Covid-19 test result has been returned by one of our playing staff.
“As a result, tomorrow's Premier Sports Cup tie with St Mirren has been cancelled. It will be awarded to the Buddies as a 3-0 victory.
“The player in question has not attended our stadium since last Saturday's friendly with Clydebank and there is no risk to anybody who has been at the stadium since then.
“We apologise for the disappointment this will cause, as we were very much looking forward to returning to competitive action with our fans in our stadium.
“However, we hope that supporters of each team will understand the need to take precautions in these circumstances, which has resulted in our application to the SPFL to have the game cancelled.”
A spokesperson for St Mirren added: “The SPFL Board has awarded a 3-0 win to St Mirren in Saturday’s Premier Sports Cup tie against Dumbarton, after the League One side informed the SPFL that they are unable to fulfil the fixture.
"Dumbarton informed the SPFL that a player had tested positive for COVID-19 and, as a result of close contacts and player injuries, they do not have sufficient players available to fulfil the fixture.
"St Mirren Football Club would like to wish the affected player all the very best in his recovery.”