Jones made three Test appearances for the 2005 Lions having been called up as a late replacement and was hoping to make a similar impact this time around after replacing Ulster flanker Stephen Ferris in the current squad earlier this week.
The 28-year-old joined the Lions in Cape Town on Thursday but a series of medical examinations highlighted the fact that he was not currently fit to play a part in the remainder of the 10-match tour.
Jones underwent the same routine medical testing as all replacement players joining up with the Lions and it led to the team's medical staff to request a further examination by an independent neurosurgeon.
This was due to a concern over his recent medical history that included two significant knocks to the head while playing for Wales on their recent tour to Canada and the Unites States of 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.
Jones is expected to fly out of Cape Town today, with Lions head coach McGeechan stating that no further replacement player will be required at this stage.
"I am very disappointed that on medical grounds I have been told that I am not currently fit enough to play an active role on the tour," said Jones.
"I was looking forward to getting involved with the rest of the lads but I guess it wasn't meant to be. It has been an up and down year for me in many ways.
"I feel okay at present but obviously I have to listen to the neurosurgeon's advice in terms of my health, and to ensure I make a full recovery."