Craig Alcock, Harry Middleton and youngster Joey McCormick all suffered serious injuries during Wednesday night's friendly with Newcastle United.
Joe Wright also hobbled off during the game and joins the likes of Gary McSheffrey, Mathieu Baudry and Paul Keegan in the treatment room.
With Rovers' youth team currently in Sweden for the Gothia Cup, Rovers would have struggled to put out a side for the trip to the Aggborough Stadium on Saturday.
Boss Darren Ferguson said: "This is not a decision we have taken lightly, but unfortunately is a football decision due to circumstances beyond our control.
"We believe this is a decision we need to take to risk no further injuries to our players.
“Having worked with and taken advice from our medical team we are confident that we will be ready to go for the August 6 away at Accrington.
“We would like to apologise to supporters for any inconvenience caused but by taking this carefully considered step, we are protecting ourselves and giving ourselves the best possible chance to prepare correctly for the forthcoming season and achieve our aims.
“We hope that the players make a full and speedy recovery; we wish them well.”
Rovers have offered to play Kidderminster in a friendly next summer.
The planned friendly at York City on Tuesday night will take place, Rovers have confirmed.