The competition, which Saints won in 2019, was scheduled to be played as a midweek tournament starting in April, but it has now been called off due to ongoing issues with the Covid-19 pandemic.
A Premiership Rugby statement read: "The Covid-19 pandemic continues to present significant challenges for sport, and following consultation with our clubs over the past few weeks we have decided to cancel the Premiership Rugby Cup for this season.
"Alternative options were considered but all raised concerns around the safety of players and the risk of games not being completed, so in the light of these player welfare and competition integrity concerns the cup cannot proceed this season.
"The 2020-21 Premiership Rugby Cup was planned as a development competition, but it was clear that in this unique season it would not be possible to add additional players to playing squads and properly prepare them for competition without compromising the clubs' Covid-19 training bubble which everyone has fought so hard to protect."
Meanwhile, the date has been set for Saints’ Challenge Cup last-16 clash with the Dragons.
Chris Boyd’s side will go to Rodney Parade on Saturday, April 3 (k/o 5.30pm).
The game will be shown live on BT Sport
The winner of the tie will host Harlequins or Ulster in the quarter-finals on the following weekend.
Two Premiership fixtures have also now been set in stone, with Saints hosting London Irish on Friday, April 16 (kick-off 7.45pm) before travelling to Leicester Tigers on Saturday, April 24 (kick-off 3pm).
Those matches will also be live on BT Sport.