The Real Madrid legend has reportedly been taken to hospital after suffering a heart attack.
Porto confirmed the news to Portuguese television channel TVI. Casillas is expected to be ruled out for the rest of the season.
The Porto shot-stopper, 37, recently signed a new contract with the Primeira Liga club until 2022.
Casillas is widely considered to be one of the best goalkeepers in his generation.
As former Spain and Real Madrid captain, he led Los Blancos to win five La Liga titles and three Champions League titles as well as the national team to win the World Cup 2010 and EURO 2008 and 2012, finishing a historic treble for La Roja.