Officers responding around 11:30 a.m. Wednesday to reports of a medical emergency found the 47-year-old Giambi dead at the residence, said Lt. Robert Ewing of the Claremont Police Department.
The Los Angeles County Coroner's Office determined the cause of death to be suicide after Giambi suffered a gunshot wound to the chest.
Giambi's agent, Joel Wolfe, said the family requested "that we all respect their privacy during this difficult time."
A brother of five-time All-Star Jason Giambi, Jeremy Giambi spent six seasons in the major leagues as an outfielder and first baseman with Kansas City (1998-99), Oakland (2000-02), Philadelphia (2002) and Boston (2002-03).
Jeremy hit .263 with 52 homers and 209 RBIs. His best season was 2001, when he batted .283 with 12 homers and 57 RBIs for the Athletics.
If you are struggling with thoughts of suicide, or worried about a friend or loved one, help is available. Call the National Suicide Prevention Lifeline at 1-800-273-8255 (TALK), or text TALK to 741-741 for free confidential emotional support 24 hours a day 7 days a week.
The Associated Press contributed to this report.