"This is a wonderful and difficult day,'' said Masters chairman Billy Payne. "Arnold Palmer was more than a king. He was my friend. He was your friend.''
Palmer died in September and Nicklaus spoke at memorial services. He said Tuesday, "life goes on, but it's not the same."
Nicklaus and Player wiped tears during a moment of silence before they approached the tee box for the traditional tournament-opening shots without Palmer for the first time since 2007. Nicklaus joined Palmer for the ceremony in 2010 and Player in 2012.
"The Masters did make Arnold in many ways because of his wins in '58, '60, '62 and '64. But in another way Arnold made the Masters," Nicklaus said. "I think Arnold put the Masters on the map. They were very good for each other."
Combined, the legendary trio won 13 Masters.
Honorary starters were first used at Augusta National in 1963.
This is the first Masters Tournament without Palmer since 1954.
Palmer's widow, Kit, was present along with many golfers in the tournament field.