Jimmy Kimmel was on the verge of tears during his opening monologue Monday as he described the terrifying experience immediately after the birth of his son ... who needed life-saving heart surgery.

Jimmy's son, Billy, was born a little over a week ago and seemed fine at first ... but hours later was diagnosed with a heart condition that required open heart surgery.

The comedian says Billy's pulmonary valve was completely blocked, and he also had a hole in the wall between the left and right sides of his heart. His first open heart surgery was apparently a success ... but Jimmy says he'll have to have more operations in the future.

It's a pretty emotional clip ... grab the tissues.