The 45-year-old, who spent two seasons at Newcastle, said he has been forced to leave his home town of Tulua because of fears for his safety.
Asprilla was reportedly threatened by four men in two cars on Tuesday.
Faustino Asprilla (talking to the El Tiempo newspaper): "They told me to contact their chief because if I didn't they would kill my family and me.
"Today is one of the saddest days of my life. I had to leave my own land, Tulua, as a victim of extortion by a group of anti-socials.
"My family was threatened in front of me, my father, my sisters. Helpless and hurting, I took the decision for the safety of my loved ones to leave Tulua.
"I dedicated my life to representing my country abroad, to bringing joy to my Colombian people, when I could finally rest, to recover the time lost with my (family), I'm forced to leave by the back door of my own town."