Simpson, 54, who joined City as assistant head coach under former manager Dean Holden in August 2020, will undergo treatment for kidney cancer.
The Sky Bet Championship club said on their official website: "Paul Simpson is taking time out from his coaching role to have treatment for renal cell carcinoma.
"The Robins' assistant coach will finish his duties temporarily at the end of this week.
"Everyone at City wishes Paul all the best for his treatment and recovery and looks forward to welcoming him back. Academy coaching staff will support the first team during Paul's absence."
Renal cell carcinoma (RCC) is the most common form of kidney cancer in adults and forms in small tubes within the organ.
Former Manchester City, Derby and Oxford winger Simpson guided England Under-20s to World Cup glory as head coach in 2017 and has also had managerial spells at Rochdale, Carlisle, Preston, Shrewsbury and Stockport.