A bullet is lodged in his left hip.
Mr Munyes, who spent Sunday night at Lodwar district Hospital in Turkana, was airlifted to the Nairobi Hospital for surgery to remove the bullet.
He arrived at Wilson Airport aboard a private jet at midday and taken to the Nairobi Hospital by a Kenya Red Cross ambulance.
Mr Munyes was part of a peace delegation to Ethiopia comprising among others Turkana Governor Josphat Nanok and county police commander Emmanuel Karisa.
Turkana North MP Christopher Nakuleu and Members of the Turkana County Assembly were also part of the delegation.
The accident happened at Loarengak in Turkana North when the senator stopped to talk to Mr Nakuleu.
Cord leader Raila Odinga visited the senator, who is also the Ford Kenya secretary general, an hour after he was admitted to hospital.
“I have been here to visit Mr Munyes, who was involved in an shooting incident, and I have talked to him as well as doctors attending to him and they have assured us that he will be fine,” said Mr Odinga who was accompanied by Tongaren MP Eseli Simiyu.
Dr Simiyu said the senator was shot accidentally and that the bodyguard was remorseful because he had no intention of harming the former Cabinet minister.
“He was in Turkana for three days of peace building and given the area is high risk, their guns were cocked,” said Dr Simiyu.
The gun discharged a bullet accidentally. The bullet hit a metal object and bounced back, hitting the senator in the hip.
The bodyguard was sitting behind the senator in a car at the time of the accident.