Casillas, 37, who captained Spain when they won their only world cup in 2010, suffered an acute myocardial infarction on Wednesday morning at the PortoGaia Training Center in Olival.
The session was immediately suspended as Casillas was rushed to the Hospital CUF in the city, before the club later confirmed the heart problem had been “solved”.
Casillas tweeted on Wednesday evening: “All under control here, a big scare but with the forces intact. Thank you very much for the messages and affection.”
Former Real Madrid teammate Sergio Ramos, Wales international Gareth Bale and Newcastle manager Rafa Benitez were among those wishing him well.
The link between footballers and cardiac arrest has come under increasing scrutiny in recent years following a number of deaths.
Cameroon international Marc Vivien Foe was 28 when he died after collapsing on the pitch in the Confederations Cup in 2003.
Fabrice Muamba was also taken ill while playing for Bolton in 2012 and his heart stopped for 78 minutes before he recovered.
In 2015 and 2016, non-league players Junior Dian and Danny Wilkinson both died during games and the following year, former England defender Ugo Ehiogu, who was a Spurs coach, died aged 44.
It has led to calls for all young people involved in sport to be screened for underlying heart conditions.
Casillas, who won 167 caps for his country, turns 38 later this month.
He won the Champions League three times with Real Madrid, where he spent most of his career and signed a new deal with Portuguese club Porto in March, having moved there from Real in 2015.
Porto are currently second in the table, two points behind Benfica with three games remaining, as well as in a cup final clash against Sporting Lisbon.
