The Spaniard, who once considered playing for England after being overlooked by his home country, was close to joining Serie A side Cagliari earlier this month.
He was a free agent having played the past two years at Watford.
However, Cagliari abandoned the signing of the 37-year-old after medical examinations revealed a heart problem.
"I can confirm that Manuel Almunia failed a medical due to a heart condition," Cagliari spokesman Alessandro Steri said.
"Further tests done have revealed he is suffering from an apical hypertrophic cardiomyopathy (HCM)."
HCM is a genetic heart disorder that can cause sudden death.
Almunia began his playing career at home club Osasuna in 1999. He joined Arsenal in 2004 from Celta Vigo, leaving in 2012.
The Professional Footballers' Association confirmed Almunia will not play again.
The PFA stated on Twitter: "Manuel Almunia has had to retire after being diagnosed with a heart condition. All at the PFA wish him well for the future."