APRIL 20: The Portugal international, 37, and Rodriguez, 28, were expecting twins.
Their baby girl survived, and they said her birth "gives us the strength to live this moment with some hope and happiness".
"Our baby boy, you are our angel. We will always love you," they wrote.
In a statement on social media, they said: "It is with our deepest sadness we have to announce that our baby boy has passed away.
"We are all devastated at this loss and and we kindly ask for privacy at this very difficult time."
The pair had announced the pregnancy in October.
Manchester United tweeted: "Your pain is our pain. Sending love and strength to you and the family at this time."
And team-mate Marcus Rashford said on social media: "Thoughts are with you and Georgina brother I'm so sorry."
Manchester United later confirmed Ronaldo will miss Tuesday evening's match against Liverpool.
A fan-led minute's applause will be held in the seventh minute of the game at Anfield, while both teams will wear black armbands.
"Family is more important than everything and Ronaldo is supporting his loved ones at this immensely difficult time," the club said.
"As such, we can confirm that he will not feature in the match against Liverpool at Anfield on Tuesday evening and we underline the family's request for privacy.
"Cristiano, we are all thinking of you and sending strength to the family."
Ronaldo's former side Real Madrid said the club, their president and board of directors "are deeply saddened" by the news, adding: "Real shares in the family's pain and wishes to send them all of our warmth."
Manchester City, Leeds United and the Premier League have also tweeted messages of condolence.
Ronaldo has a son, Cristiano Jr, who was born in 2010, and twins Eva and Mateo who were born in 2017. He also has a daughter with Rodriguez, Alana Martina, who was born in 2017.
