The Spaniard, 37, was set to join Serie A side Cagliari on a free transfer after two seasons at Watford.
Tests revealed Almunia, who played 175 times for Arsenal, has a potentially fatal genetic heart disorder.
“I can confirm that Manuel Almunia failed a medical due to a heart condition,” said a Cagliari spokesman.
Apical hypertrophic cardiomyopathy is a disease of the heart tissue that causes it to thicken and can lead to sudden death.
Almunia began his playing career at home club Osasuna in 1999 before joining Arsenal in 2004 from Celta Vigo, leaving eight years later for Watford.
He replaced first-choice keeper Jens Lehmann in the 2006 Champions League final against Barcelona when the German was sent off in the first half. Arsenal lost the game 2-1.