Nadal is currently on an exhibition tour in Central and South America with top Norwegian player Casper Ruud.
Nadal, 36, played doubles with Federer on the first day of the Laver Cup, the Swiss's last appearance in a competitive match.
Nadal also ended the tournament after that match to assist his wife with the birth of the couple's first child, who was born in mid-October, Rafael junior.
Both Nadal and Federer were moved by the moment and tears flowed as they sat hand in hand.
- You know you will never be with anything like that again and a part of my life disappeared with him.
It was also emotional to say goodbye to someone who has been so important to our sport, Nadal told Reuters in Argentina.
"More important things than tennis"
They met a total of 40 times and Nadal won 24 of the meetings.
Nadal won the first two Grand Slams of the season – in Australia and in Paris, but at the same time has had major problems with injuries.
He was out for several weeks with a rib injury ahead of the clay court season and received painkiller shots for foot pain ahead of his 14th title at Roland Garros.
A stomach injury forced him to throw in the towel ahead of the semi-final against Nick Kyrgios at Wimbledon.
- My time will come when it is.
It won't be a problem for me.
My life has changed so that there are things that are as important or more important than tennis, says the new father.
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Roger Federer burst into tears and hugged his family after his retirement from professional tennis last night.
Photo: Kin Cheung/TT