"Real Madrid wants to transmit all their support to their beloved captain Casillas," the statement read.
"Casillas has taught us throughout his professional career to overcome the most incredible challenges to enhance the glory of our club.
"It has taught us that giving up does not fit into our philosophy of life and has shown us countless times that being stronger, the harder the challenge, is the way to achieve victory.
"Real Madrid want to see their eternal captain recovered as soon as possible and send him all the courage of the world."
A Spanish footballing icon
Casillas is held in high esteem at the Bernabeu, with the 13-time European champions describing him as "the best goalkeeper in our history" on their official website.
Born a short distance from the stadium, he graduated from the youth ranks, and the 'C' and 'B' teams, to establish himself as a regular first-team player, winning 10 major titles during a 16-year career with Los Blancos.
The former club captain, who moved to Porto on a free transfer in 2015, holds the distinction of having made the most Champions League appearances of any player - 176 - and became the first player to appear in 20 consecutive seasons of the competition.
Casillas is also the most-capped Spain player, having made 167 appearances.
He helped Porto win the Portuguese title last season.
