The former Leigh, St Helens and Wigan boss confirmed in a statement on Monday his 19-year-old child, Robbie, died suddenly on Sunday of "adult death syndrome".
He was taken ill at his home in Leigh and rushed to Bolton Hospital where he died later.
Millward, who is in his first season with the Tigers, was returning to England with his team following Saturday's Super League clash against Catalan Dragons in Perpignan when he heard the news.
Millward said: "On behalf of all our family, we would like to thank everybody for their kind messages of support, especially the rugby league family from both the UK and Australia.
"The messages have been of comfort in this time of great sadness."
He added: "Robbie was a healthy young boy who died from a condition called sudden adult death syndrome, which comprises of a massive heart attack.
"The sudden nature of his death is making it even harder for us to deal with.
"We ask that journalists allow us the space and time needed to come to terms with the loss of Robbie.
"Instead of flowers, we ask any well-wishers to donate to the British Heart Foundation."
RFL chairman Richard Lewis said: "On behalf of the whole rugby league community, I would like to express our deepest sympathy to Ian, his family and Robbie's friends at this terrible news.
"The thoughts of everyone involved in the sport are with the Millward family and friends at this very sad time."