The Ospreys and Wales back rower underwent the same routine medical testing as all replacement players joining the tour go through.
It led to the squad's medical staff requesting a further examination by an independent neurosurgeon.
This was due to a concern over the player's recent medical history that included two significant knocks to the head while playing for Wales during their recent tour to North America.
On the advice of the neurosurgeon it was determined that it was not safe for Jones to undertake any physical contact for a mandatory three weeks.
This is in line with IRB Regulation 10.1 on concussion.
It is anticipated that the Wales captain will fly out of Cape Town today (Friday). Lions head coach Ian McGeechan has stated that, at this stage, no further replacement player will be required.