Allardyce set to have heart surgery
The Rovers website said Allardyce, 55, would undergo an angioplasty next week to correct a narrowing to a branch of his coronary arteries after recently complaining of chest discomfort.
Allardyce will miss Sunday's game against his former club Bolton Wanderers as well as matches against Fulham (away) and Stoke City (home).
Assistant manager Neil McDonald will take charge of the first team in his absence.
"His well being is of prime consideration," said Rovers' chairman John Williams.
"We all appreciate that Premier League football is a stressful business and prevention is always better than cure."