Video report by ITV News Health Correspondent Emily Morgan
In a letter written to NHS staff, Mr Hancock said: “If a patient asks to be treated by a white doctor, the answer is ‘no’.
"Your management must and will always back you up.”
He wrote he was “horrified” by accounts of the abuse staff face and said it is “absolutely appalling” that many of these incidents are racially motivated.
The testimony of Radhakrishna Shanbhag, who spoke to ITV News last week and was reduced to tears when recalling how patients have spoken to him, was particularly powerful and referenced by Mr Hancock.
Mr Shanbhag said that such was the level of abuse he had suffered, he would have left the NHS long ago had it not been for the fact he has to provide for his 12-year-old daughter.
He recalled an incident where a patient requested a white doctor, and so they were sent home and booked in for another day.
He added he has been sidelined and ignored by patients, and treated by some as if he should not be in the hospital.
He said it makes him feel “worthless”.
Writing to NHS staff, Mr Hancock said: “Like me, you may have seen the shocking testimony of Radhakrishna Shanbhag, a hard-working doctor who has committed more than 20 years of his life to the NHS.
“I want to send a clear message, from the very top of our health and care system, with the strong support of the entire national leadership of the NHS: this sort of abuse is unacceptable and we will not tolerate it.”
It is unclear at this stage if this will become official government policy but Mr Hancock added that “no one is entitled to choose the colour of the skin of the person giving that healthcare”.
It is also unclear if the NHS can refuse to treat patients if they insist they will only be seen by a white member of staff.
Last week, Mr Hancock stopped short of backing calls to withdraw treatment to patients who use racially abusive language or refuse care from a black or minority ethnic clinicians.
He added: “I therefore expect that all appropriate steps are taken by organisations to ensure their staff know they can come to a workplace that is free from abuse and harassment.”
Labour leader Jeremy Corbyn has also joined in widespread condemnation of the rising tide of racist abuse, calling the abuse Mr Shanbhag had received "horrific".
Mr Hancock also wrote a separate letter to Mr Shanbhag, saying he was "shocked and really saddened" after seeing his interview with ITV News.
"But the thing that made me really angry was the fact you didn’t know if you’d be backed up by your bosses if you acted," the 41-year-old said.
He added he wanted to "thank" Mr Shanbhag.
"Thank you for a life of service to others, for your service to the NHS, and for being brave in speaking out on the media.
"I salute you, and let us work together to end the evil of racism."
Dr Shanbhag was not the only NHS employee to tell ITV News of the racist abuse they have suffered.
Others said they had been called things such as "little China girl", "P*** doctor" and "black b****".
So casual are the comments, one nurse said, she doesn't even bother to report them.