United confirmed the Dutch midfielder's contract had been "terminated by mutual agreement" for health reasons.
Sneijder, the younger brother of Holland midfielder Wesley, made one appearance for the club, coming off the bench in their opening Ladbrokes Premiership defeat by Aberdeen on August 2.
Three days later he returned to Holland for tests on an illness and his departure has now been confirmed.
United manager Jackie McNamara said: "This is the best solution for Rodney first and foremost.
"We have a responsibility to protect the player's health moving forward and respect his current situation."
The club statement added: "Everyone at Dundee United wishes Rodney all the very best for the future.
"The club will replace any replica shirt which has been purchased from Dundee United Direct and customised with the player's name."
Sneijder could soon be followed out of Tannadice by Henri Anier, who has gone on trial with Polish side Wisla Krakow.
The Estonia striker joined United in January from German side Erzgebirge but failed to replicate the form he showed at Motherwell and has not even made the United bench this season.
Source : PA