Aberdeen City Council apologised for the uncertainty caused by the claim, relating to the city's Hazlehead Crematorium.
New Aberdeen City Council chief executive Angela Scott said the findings of an earlier independent audit into practices and procedures at Hazlehead would now have to be reconsidered.
Families alleging the wrongful disposal of baby ashes in Aberdeen said they were shocked by the latest development.
Paul Wells, whose infant son Scott died in 2006, said he was devastated by the news, adding: "To think that something like this could have happened to my son Scott, well it's the worst possible scenario.
"We have dreaded something like this. It's more than someone not doing their job properly. The lies are all starting to come out now, it is all unravelling."
Patrick McGuire of Glasgow-based Thompsons Solicitors, who represents many of the families affected, said: "The families I represent are almost broken by this news. Any suggestion that infants and adults have been cremated together must be rigorously investigated.
"At almost every stage Aberdeen City have tried to block or evade attempts by the parents to find out what happened to their babies' remains. This has got to stop now."
It comes at a time of ongoing scrutiny of practices at crematoria in Scotland.
In April, former Lord Advocate Dame Elish Angiolini published an extensive report into historic practices at Edinburgh's Mortonhall crematorium and concluded that hundreds of bereaved parents whose babies had been cremated there faced a lifetime of uncertainty over what happened to their children's remains.
Dame Elish said any crematorium that cannot guarantee ashes to return to bereaved families should stop cremating babies.
A separate independent commission, led by former High Court judge Lord Bonomy, has been reviewing policies and practice across Scotland in relation to the handling of ashes after the cremation of babies and infants.
Last summer a PricewaterhouseCoopers report on Hazlehead found that from April 1, 2007 to December 31, 2012 there were 40 cases where no ashes were retrieved when infants aged under two had been cremated.
But last month Aberdeen City Council admitted changing how it cremates young children in the wake of the scandal. It said that since November last year ashes have been recovered in all cases and returned to the family or scattered as per request.
In a statement issued by Aberdeen City Council, Ms Scott said: "As you know, the working practices of crematoria across Scotland have been under scrutiny recently. Throughout this time, Aberdeen City Council has endeavoured to be open and transparent about its own procedures at Hazlehead Crematorium.
"For this reason, I wanted to let you know that I have received a serious allegation regarding practices at Hazlehead Crematorium. The allegation relates to the joint cremation of babies and adults."
The council has not indicated the dates to which the claim refers, or how many cases are allegedly affected.
Ms Scott acknowledged public interest in the matter would be high and asked for time to carry out a thorough investigation.
"I will, of course, share relevant information once I have it," she added.
"On behalf of Aberdeen City Council, I want to take this opportunity to apologise for the further uncertainty that today's announcement creates.
"I also want to take the opportunity to reassure members of the public that they will continue to receive a kind and caring service at Hazlehead Crematorium."