A spokesman said the former chief executive officer of the FSA would be taking a break “because he is not very well” until the New Year, when he intends to return.
It was also confirmed that Sir Hector will continue to receive full pay and pension contributions during his absence.
Sir Hector joined Barclays as head of global compliance on a reported £3m remuneration package at the end of last year.
It followed a five-year tenure at the helm of the FSA. He resigned from the regulator three months before it was dissolved and split into two new watchdogs.
It is the second upheaval in senior ranks at Barclays in the space of two months. In August, group finance director Chris Lucas permanently stepped down, six months earlier than planned, due to his deteriorating health.