The John Radcliffe Hospital is investigating the deaths of four children who underwent heart operations there in recent months.
The Oxford hospitaL has suspended children's cardiac surgery until the investigation has been concluded.
Parents of 26 children due to undergo operations at the Children's Hospital based there are being contacted. Those who need urgent treatment are to be transferred elsewhere.
The deaths of the "very sick children" happened either during or after surgery. The hospital is yet to release further details about the fatalities.
A spokesman for the Oxford Radcliffe Hospitals NHS Trust said: "We have temporarily suspended the paediatric cardiac surgery service while we investigate concerns that have been raised.
"Our investigations are likely to include an external review of the deaths of some very sick children (four children) who underwent surgery at the John Radcliffe Hospital in the last three to four months.
"The families of children awaiting cardiac surgery are being contacted and we will be placing those patients who need to be seen urgently with other hospitals. We are reviewing each of these patients to ensure that they are not put at risk by any delay in their treatment."
Deaths after children's heart surgery at the hospital fall within normal ranges and there has been no previous cause for concern.
The Care Quality Commission said it was monitoring the situation closely.
A CQC spokesman said: "We will monitor this situation extremely closely.
"It is reassuring that the trust has taken action to ensure the immediate safety of patients.
"This is high-risk surgery and the trust is taking the right steps in conducting a review."
Patients and their families are asked to contact the hospital on 01865 741166.
The president of the Society of Cardiothoracic Surgery, Leslie Hamilton, said that children needing heart surgery would be sent to one of the country's ten other specialist units while the Oxford service is suspended.
He told BBC Radio 4's Today programme: "They will look at the whole package of care. It will take a period of time to set up a review because they will want people from outside to come in and look at things, and that will be practising surgeons and cardiologists from other units.
"It will take some time, which is why, I presume, they have suspended surgery until they are happy they can explain things."
Mr Hamilton said that the decision to suspend services was probably taken by the hospital's medical director.
"He will have been aware of the events and have taken a very difficult decision, but he will always err on the side of patient safety," he said.
"When any child dies after heart surgery, it has a devastating affect on the team and obviously if there were a couple of deaths in short succession, this will have been a big factor."
Health Secretary Andy Burnham told Sky News: "Obviously, the hospital have done the right thing by acting quickly to suspend further surgery.
"I think the important thing to say is this is very high-risk surgery. It's often dealing with some very poorly children indeed.
"I think it's important to put that context out."
He said parents should be reassured by the speed in which an inquiry was launched by the hospital.
"They have acted correctly and, obviously, they will conduct their investigation as quickly as possible," he said.
"I think parents should be reassured by the fact that the hospital have been reviewing their data and have acted quickly.
"The pattern may be explained by other reasons, I don't know. The right thing here is not to pre-judge that investigation."
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