Shoebridge paid the price for his failure to award Crystal Palace a perfectly legitimate goal in the game at Ashton Gate on Saturday as Tuesday's league clash between Plymouth and Cardiff at Home Park was taken from him.
His assistant Chris Knowles was also removed from taking charge of the game.
Palace striker Freddie Sears looked to have given his side the lead after 34 minutes when he drilled a low shot into the corner of the net.
Shoebridge inexplicably awarded a goal-kick with neither himself or the assistant spotting the ball had crossed the line.
Hackett, general manager of the Professional Game Match Officials Board, said told BBC Radio Five Live: "There's no doubt he'll be fretting away but we will give him the support to rebuild him and get him back fresh for his next appointment.
"I think it will be a couple of weeks before we bring him back.
In the meantime he'll have the appropriate discussion and debate with his codes in order to analyse very carefully why it was missed.
"He probably was out of position, should have been thinking about that."