Bodies are now being examined at other sites during the suspension, which began last Thursday.
The Human Tissue Authority said two licences were suspended after an inspection last month showed poor compliance with regulatory standards.
Dr Sandy Mather, director of regulation at the HTA said, "Our inspections focus on mortuaries and the systems that are in place to ensure post-mortem examinations take place in suitable facilities by trained staff working to stringent procedures. This regulation is needed to protect the interests of the public and professionals; and helps maintain their confidence.
"The inspection showed poor compliance with HTA standards giving rise to serious concerns about practices and procedures relating to post-mortem examination. We therefore took the decision to suspend two HTA licences. This means that post-mortem examinations cannot take place at the hospital mortuary at present.
"The notice of suspension was issued on August 13 and came into effect immediately. We have been in dialogue with the chief executive and other senior members of staff at the hospital since the inspection and we are confident they understand the serious nature of this action. "
Jan Williams, who took up the post of chief executive of Cardiff and Vale NHS Trust in July, said: "I am disappointed to come in and find myself in receipt of the HTA report - "I accept fully the report's findings and recommendations and have taken immediate action to ensure that we address the concerns raised swiftly so that our licence suspension can be lifted as soon as possible.
"In addition, I have set up an urgent inquiry into the circumstances that led to the HTA decision, to be conducted by Healthcare Inspectorate Wales.
"The nature of mortuary work means that should something go wrong, it has the potential to cause significant distress to those involved; it is therefore essential that establishments comply with HTA regulatory requirements."
Conservative Shadow Health Minister Andrew RT Davies said: "This once again calls into question people's confidence in the service made available by Cardiff and Vale NHS Trust.
"With the trust currently trying to make Ģ60mn of efficiency savings - this is another blow to staff morale and patient confidence.
"Suspending post-mortem examinations is an extreme step to take and the Human Tissue Authority would not make it lightly.
"Whatever the problems are at the mortuary they need to be rectified as soon as possible.
"Transferring bodies is not only putting pressure on other hospitals but is also extremely distressing for bereaved families."
A Welsh Assembly Government spokesperson said: "People should be assured that where the HTA identifies any non-compliance, action is taken quickly to tackle the problems.
"The Welsh Assembly Government has sought and received assurances from Cardiff and Vale NHS Trust that it has put in place measures to ensure continued access to post-mortem services.
"We expect the trust to address immediately all the concerns raised by the Human Tissue Authority so it can regain the license for the University Hospital of Wales mortuary facilities.
"The trust has set up a team led by the trust's new chief executive Jan Williams to drive forward the necessary changes."