Scottish Labour's health spokesperson Monica Lennon said that the claims, made by a whistleblower at the Queen Elizabeth University Hospital, needed to be answered immediately by the Scottish Government.
It has been reported the child's parents were not told about the contaminated water, which emerged following investigations into infections in children in the cancer wards at the Royal Hospital for Children (RHC) in Glasgow in 2017.
Two wards at the RHC were closed last September and patients moved to the adjoining Queen Elizabeth University Hospital (QEUH) as Health Protection Scotland (HPS) investigated water contamination incidents.
An HPS investigation found 23 cases of blood stream infections with organisms potentially linked to water contamination were identified between 29 January and 26 September 2018.
The whistleblower contacted Scottish Labour MSP Anas Sarwar, claiming this investigation found up to 26 cases of water supply infections in children in the cancer wards in 2017, and that one child with cancer died after contracting an infection. The allegation was also made that the child's parents had not been informed about the infection.
Mr Sarwar raised the issue with Nicola Sturgeon at First Minister’s Question today, asking her to personally intervene. She said she "could not begin to imagine the pain of those who had lost loved ones".
She added: "Patient safety is paramount and that's exactly why the health secretary commissioned the independent review into the design, build, commissioning and maintenance of the QEUH and its also why, on 18 September, a public inquiry into the issues at the hospital and the Sick Kids Hospital in Edinburgh was announced.
"We are determined to address the concerns of patients and families and the Health Secretary is committed to returning to Parliament to set out the full details of the public inquiry as soon as possible."
However Mr Sarwar said he was disappointed in her response, which "failed to address the serious issues raised" and implored the First Minister "to reflect on this and personally intervene to seek answers, get justice for the families, and take the necessary actions so this never happens again.”
Now his colleague, Monica Lennon has written to the Health Secretary Jeane Freeman urging her to "demand immediate answers" from NHS Greater Glasgow and Clyde.
She also requested that families who need information and answers are provided with a clear, dedicated contact or helpline.
“This is an extremely serious allegation and Nicola Sturgeon’s reaction at First Minister’s Questions does nothing to reassure worried parents and the wider public or cut through the evasive statement issued by NHS Greater Glasgow and Clyde," she said.
“Jeane Freeman must pursue answers from NHSGGC immediately and an urgent probe must get underway. Support must be made available to bereaved parents, including either a dedicated contact or helpline for families who need answers.
“The public inquiry into the wider scandals at the QEUH, that Scottish Labour successfully campaigned for, must get underway very soon. Public confidence in our hospitals is being put to the test and SNP Ministers must urgently respond to this latest serious allegation.”
NHS Greater Glasgow and Clyde insisted its "overriding priority" is the safety of its patients, and that tests have shown the water supply is safe.
An spokesman said: "We rigorously review all cases of infection to ensure that our patients are appropriately cared for. We also completed an additional clinical review of the cases from 2017 in July 2019. This was carried out by senior clinical staff and it was concluded that no further action was required.
"Further to this, we have been working closely with external advisers Health Protection Scotland, assisted by Strathclyde University, on a review of cases of infection over a period from January 2015 to September 2019 and this report is due imminently.
"It is important to make clear that the water supply to the Royal Hospital for Children and Queen Elizabeth University Hospital is safe to use."
It said "extensive measures" have been put in place and the water has been assessed by an independent expert who confirmed it is "wholesome", meaning it is safe to use.
The health board said when a patient dies, clinical teams discuss with family members the cause of death and the factors that have contributed to this, where they are known.