X-rays were found scattered about the building, which was closed in 2001
Calls have been made for all abandoned Scottish hospital buildings to be examined, after private patient data was found at a disused site in Carluke.
BBC Scotland revealed that X-rays marked with patients' names, photographs and other paperwork were found at the derelict Law Hospital.
NHS Lanarkshire admitted mistakes were made in transferring the information between sites and issued an apology.
In May records were found at a disused hospital in Dundee.
The Lib Dems and Labour said derelict sites should be examined to prevent such an incident happening again.
The finding came to light after amateur photographer Gary Whittle sent shots of the hospital to the BBC Scotland news website.
Mr Whittle said he and three friends, who have an interest in taking "atmospheric" photographs of abandoned buildings, were simply able to walk into the hospital.
BBC Scotland's health correspondent Eleanor Bradford went into the abandoned buildings to look at the records
The incident comes two months after it emerged that children's medical records had been left in the abandoned Strathmartine hospital in Dundee.
They included details about a girl's adoption and a child with foetal alcohol syndrome.
Following the latest discovery, Liberal Democrat MSP Robert Brown said patients had again been "badly let down".
We would like to reassure members of the public that we are taking this situation extremely seriously and will undertake a full investigation
NHS Lanarkshire spokesman
"It will be an absolute disgrace if confidential patient information has been left in an abandoned hospital building since 2001," he said.
"This is the second incident of patient records being left in former Scottish hospitals this year.
"The Scottish Government must order an investigation and full audit into all former hospital buildings to ensure that there are no more patient records or information lying discarded and open to public view."
Dr Richard Simpson, Labour's health spokesman, said: "For identifiable records to be left scattered at an abandoned hospital clearly breaches the Data Protection Act.
"The Scottish Health Department is failing in its legal duty to protect patient confidentiality."
He said the incident at Strathmartine hospital should have triggered an immediate investigation to ensure there were no records left in other disused hospitals.
"As a doctor, I find the health secretary's continuing complacency about patients' medical records both alarming and unacceptable," he said.
"It is no longer sufficient for this important issue to be dealt with by an internal NHS review.
"We need a broader inquiry, completely independent of government, to ensure that patients can have confidence that more medical records will not be found abandoned anywhere else."
An NHS Lanarkshire spokesman said: "There are clear policies and processes in place when transferring patient information from one site to the other.
"There has, however, been an error which has resulted in some information being left on the site."
The spokesman said action had been taken to clear the site and extra 24-hour security measures had been put in place.
"We are confident that patient care has not been compromised," he said. "However, we would like to reassure members of the public that we are taking this situation extremely seriously and will undertake a full investigation.
"We apologise for any public anxieties resulting from this situation."
Tim Davison, chief executive of NHS Lanarkshire, has said he was "hugely disappointed" by the discovery because the health board had been told the site had been cleared.
A Scottish Government spokesman has said Health Secretary Nicola Sturgeon was concerned to hear about the incident in Carluke and has asked NHS Lanarkshire to provide her with full details of the situation as soon as possible.
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