The Real Madrid legend has recovered since Thursday's incident.
Valdes posted to social media: "Dear Iker, dear friend.
"In this world of football, some choose to be a goalkeeper; others must learn to be with their defects and virtues.
"You are and always will be an idol to those who are born with a glove in the palm of their hand. The idol that the rest must reach, the idol that those look to who when training with dreams of raising, like you, the World Cup with the No.1 on his back.
"You are, and forever will be, what every goalkeeper dreams of being. Someone capable of flying higher and longer than all the others at the same time, making the unthinkable possible, executing every action perfectly and leaving everyone sighing because of those magnificent stops.
"My friend, it's inevitable for me to get excited writing these lines remembering what I've lived, admiring with a certain nostalgia those great confrontations in which, of course, having you in front of me made me value everything much more. Without you knowing it, you gave me so much in each training session. A whole country acclaimed you in its streets.
"Dear Iker, dear friend, as goalkeepers we go without fear and that identifies us. That danger that life decides to bring to our area, and this time it's more than just simple save. Your heart, the one that beats for the sake of those who dream of reaching what you once were, claims you, and as a friend and rival from the past, I encourage you to be that white lion again.
"It's your legacy that defines you, and that is already historical.
"Always in my thoughts, from goalkeeper to goalkeeper."