Smith was hit on the right temple on the second day of the second Test against Pakistan by a Mohammed Irfan bouncer.
South Africa team manager Dr Mohammed Moosajee said in a statement: "Graeme was symptom free after the blow except for a mild headache and tests at the time allowed him to continue playing.
"However, seven days post-injury, during the second ODI in Dubai he started complaining of blurred vision which progressed to dizziness, unsteadiness on his feet and difficulty focusing.
"The MRI scan was clear, however it is in keeping with the assessment of post-concussion syndrome, which is usually a clinical diagnosis. post-concussion syndrome can be described as a collection of symptoms that some people develop after they have experienced a minor traumatic brain injury otherwise known as concussion.
"Graeme will leave the tour on Thursday, and has been advised a rest period of at least two weeks by the medical team. He will continuously be monitored in the interim."
Smith suffered the injury on October 24. The ODI series stands at 1-1, with the third match being played on Wednesday.
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