Jones was asked at a press conference on Thursday afternoon about his meditation practices having revealed in June last year that he engages in mindfulness as part of his early morning routine.
In a clumsy response that was intended as a joke and was delivered with a smile, Jones said: "I don't think I've ever spoken about meditation.
"You must be thinking about someone else... Maybe another half-Asian person... Maybe we all look the same."
Those assembled in the room were aghast at the ill-advised comment despite its context as a joke.
A private apology was later sought by the reporter who posed the question and Jones duly said sorry, shaking hands.
A Rugby Football Union spokesman said: "Eddie made an off-the-cuff comment during the press conference which was not intended to cause any offence.
"He has subsequently spoken to the journalist privately explaining this and apologised which was accepted."
Jones has taken the unprecedented step of fronting England media access every day, breaking with the protocol of placing his entire coaching team on circulation for interviews.
The Australian has been in a combative mood since his appearances first began last Thursday and a week later he continued to adopt a bellicose tone.
Immediately before being queried about meditation, Jones was asked about what steps are taken to look after the mental health of his players given the power of social media in the wake of the suicide of Love Island presenter Caroline Flack.
"That's a very interesting question. Obviously I've read and listened to some stuff on the girl and feel sorry for her family and thoughts are with the family," Jones said.
"In terms of our players we try to take a balanced approach. Obviously social media is an important part of today's society.
"To some players it's massively important, for other players it's not important. It's more of an individual way of looking after each player as well as we can."
Jones' crass joke is the latest twist in a Six Nations that has seen his methods place his four-year stewardship under pressure.
His use of the word "brutal" caused upset in France due to its connotations with violence when translated and it hardly helped England's cause as they left Paris with a comprehensive 24-17 defeat.
A week later he described Scotland as a "niggly" team due to the tactics they employed to unsettle the English at Murrayfield.
He then accused the Scotland fans of bad manners after they booed England stand-off Owen Farrell for taking so long with his place kicks.
Former Ireland captain Brian O'Driscoll this week described Jones as a "scaremonger" who over-steps the mark, although he added that he is always fascinated by his rhetoric.
England face Ireland at Twickenham on Sunday needing victory to remain in title contention.