The assailant, who has not been identified, was arrested after the failed stabbing, which took place while Mr Goïta was attending prayers in a mosque.
A government statement said the man’s health had deteriorated in custody and he was taken to hospital, where he died.
There are no particular details about his health prior to the incident.
The cause of death is said to be under investigation.
Mr Goïta has led two coups in Mali over the past year.