The veteran centre-half has lost his older brother, Steve, who was only 43.
The Blades posted: "Sheffield United is deeply saddened to hear of the passing of former player Steven Jagielka - brother of current defender Phil - at the age of 43.
"The condolences of all at the Blades are with Phil and the rest of the Jagielka family at this difficult time."
Steve played over 200 games for Shrewsbury between 1997 and 2003.
The club tweeted: "Shrewsbury Town Football Club is deeply saddened to receive news that Steve Jagielka has passed away aged 43. Our thoughts are with his family and friends at this tragic time."