Staff at Great Ormond Street Hospital have been bombarded with death threats over the case of terminally-ill Charlie Gard.
Doctors and nurses have been subjected to abuse in the street and received thousands of threatening messages in recent weeks, GOSH chairwoman Mary MacLeod said.
The hospital is in close contact with the Metropolitan Police over the incidents, she added in a statement.
The 11-month-old boy, who suffers from a rare genetic condition and has brain damage, is currently the subject of an intense legal battle between his parents and medics over his treatment.
Ms MacLeod said in a statement: "Charlie Gard's case is a heart-breaking one. We fully understand that there is intense public interest and that emotions run high.
"We recognise the tireless advocacy of Charlie's loving parents, and the natural sympathy people feel with his situation.
"However, in recent weeks the GOSH community has been subjected to a shocking and disgraceful tide of hostility and disturbance.
"Staff have received abuse both in the street and online.
"Thousands of abusive messages have been sent to doctors and nurses whose life's work is to care for sick children.
"Many of these messages are menacing, including death threats.
"Families have been harassed and discomforted while visiting their children, and we have received complaints of unacceptable behaviour even within the hospital itself.
"Whatever the strong emotions raised by this case, there can be no excuse for patients and families to have their privacy and peace disturbed as they deal with their own often very stressful situations or for dedicated doctors and nurses to suffer this kind of abuse.
"Great Ormond Street Hospital is in close contact with the Metropolitan Police, and we will do everything possible to hold to account anybody involved in this kind of deplorable behaviour."
Charlie's parents Chris Gard and Connie Yates are campaigning for their son to be allowed to undergo a therapy trial overseen by a specialist in New York.
Specialists at GOSH say the therapy is experimental and will not help. They say life support treatment should stop.
The case is due back before a High Court judge on Monday.
Keir Starmer, the constituency MP for the hospital, said: "Great Ormond Street Hospital is one of the world's leading hospitals for children.
"The staff at the hospital work tirelessly and with total dedication.
"Charlie Gard's case is truly tragic, and the whole nation sympathises with his parents. It is understandable that people feel very strongly about the case.
"But the abuse of staff at Great Ormond Street Hospital outside the hospital and online is totally unacceptable. There is no place for this abuse, and it has to stop."