The 36-year-old was expected to join French side Paris Saint-Germain but a medical examination spotted a heart problem.
But Thuram insists that his decision to retire has nothing to do with his heart problem.
"The doctors thought I had a heart problem, it is not the case. I do not have the illness," the former Barcelona man said.
"I talked to my mother, who advised me not to continue. My family wants me to stop. I did not want them to worry."
Thuram, who won a record 142 caps for France, was part of the country's squad that won the 1998 World Cup and EURO 2000.
At club level, Thuram started his career with Monaco before moving to Italian side Parma, where he won the UEFA Cup in 1999.
He then joined Juventus and won two Serie A titles there before moving to Spanish giants Barcelona in 2006.