Govorukhin was married twice. He had one son from his first marriage — Sergey Govorukhin (1961–2011), a war correspondent, writer and director of documentary films who took part in different armed conflicts in Tajikistan, Yugoslavia, Afghanistan and both Chechen wars between 1994 and 2005. In 1995 he was wounded by Chechen terrorists which resulted in one of his legs being amputated. Nevertheless, he continued his work. In 1998 he released one of the most acclaimed documentaries about the First Chechen War — "Damned and Forgotten" that was awarded with the Nika Award in 1998 as the best documentary. He also took part in several non-governmental organizations dedicated to helping disabled war veterans. In 2011 he survived a stroke and died several days later at the age of 50. He left two sons and one daughter.