The Health Secretary told the Commons there were concerns in the medical profession that "we may not be giving a voice" to doctors and other clinicians who want the "freedom to be able to learn from mistakes".
MPs heard Professor Sir Norman Williams, Mr Hunt's senior clinical adviser and former president of the Royal College of Surgeons, would conduct the "rapid review" into the application of gross negligence manslaughter in healthcare.
The report is expected to be with Mr Hunt before the end of April this year.
Announcing the review to MPs, Mr Hunt said "huge concern" has been caused by the case of Dr Hadiza Bawa-Garba, who was given a suspended jail sentence after being found guilty of gross negligence manslaughter over the death of Jack Adcock, from Glen Parva, Leicestershire.
The six-year-old, who had Down's syndrome and a known heart condition, died at Leicester Royal Infirmary in 2011 after he developed sepsis.
The prosecution argued during the trial that Jack died after a series of failings by medical staff, including Dr Bawa-Garba's "failure to discharge her duty" as the responsible doctor.
But it also claimed staff shortages meant Dr Bawa-Garba was forced to undertake the roles of three or four doctors, and a subsequent investigation at Leicester Royal Infirmary confirmed serious systemic failings at the hospital.
Speaking in the Commons, Mr Hunt said: "Working with senior lawyers, Sir Norman will review how we ensure the vital role of reflective learning, openness and transparency is protected so that mistakes are learnt from and not covered up, how we ensure there is clarity about where the line is drawn between gross negligence manslaughter and ordinary human error in medical practice so that doctors and other health professionals know where they stand with respect to criminal liability or professional misconduct, and any lessons that need to be learnt by the General Medical Council and other professional regulators."
Earlier in the same questions session, Labour accused the Government of plunging the NHS into the "biggest financial squeeze in its history".
Shadow health and social care secretary Jon Ashworth said: "Integration of health and social care needs more funding and yet the NHS is going through the biggest financial squeeze in its history and social care has been cut by billions since 2010.
"The minister a few moments ago said the funding is adequate but if funding is adequate why then are delayed discharges of care up 50% since 2010?
"If funding is adequate across health and social care why did NHS England on Friday say for the rest of this year the A&E target has effectively been abandoned?"
Health and social care minister Caroline Dinenage said an extra £2 billion funding had been made available to local authorities in the short-term, adding: "In the medium-term we need to make sure that best practice is observed across all local authorities and NHS trusts and of course in the long-term we will be coming forward with a green paper on social care later on this year."