The Bolton full-back announced his retirement on Tuesday at the age of 29.
Former Liverpool manager Benitez gave Darby his debut in a 1-1 Champions League draw with Atletico Madrid in 2008.
He made seven appearances for the Reds before joining Bradford in 2012.
Newcastle boss Benitez wrote on Twitter: "I was proud to give Stephen Darby his Liverpool debut and now I am deeply saddened to learn of his retirement. Stephen is a special person and he has my total support. He will never walk alone."
MND is a degenerative condition that affects how nerves in the brain and spinal cord function and there is not current cure.
Darby was captain of Liverpool's FA Youth Cup-winning side in 2006 when they beat a Manchester City team which included Micah Richards and Daniel Sturridge.
He made his full Liverpool debut against Fiorentina in 2009 before spending five years at Bradford, joining Bolton in 2017.
Darby, who is married to England Women's captain Steph Houghton, made five appearances for the Trotters but has not played since December last year.
Bolton boss Phil Parkinson, who also managed him at Bradford, told the Bolton News: "It is very typical of Stephen that he came in to speak with the lads and be upfront with it all, because he doesn't want them to think they cannot talk to him about his illness.
"In my time in football, he is one of the very best characters I have come across.
"He met with the specialist on Wednesday and was perhaps expecting the news that he would have to retire, but not this.
"He wanted to tell family and friends over the weekend but then get it out in the media today because people were asking questions about why he wasn't training.
"We can only offer our support. I have talked to him about keeping him involved, coming into the training ground, and he's keen to do that because there is a lot he can offer us. He can help us in many areas."