A heavy drinker and a four-pack-a-day smoker, Janssen died of a heart attack in the early morning of February 13, 1980, at his home in Malibu, California at the age of 48. At the time of his death, Janssen was filming the television movie Father Damien. Janssen was buried at the Hillside Memorial Park Cemetery in Culver City, California. A non-denominational funeral was held at the Jewish chapel of the cemetery on February 17. Suzanne Pleshette delivered the eulogy at the request of Janssen's widow. Milton Berle, Johnny Carson, Tommy Gallagher, Richard Harris, Stan Herman, Rod Stewart and Gregory Peck were among Janssen's pallbearers. Honorary pallbearers included Jack Lemmon, George Peppard, James Stewart and Danny Thomas.