They say one potential cause of the illness could be adenoviruses, but they have not ruled out Covid-19 as a cause.
Officials are examining 49 cases in England, 13 in Scotland and 12 across Wales and Northern Ireland.
The UK Health Security Agency (UKHSA) said parents should be on the lookout for symptoms such as jaundice.
Dr Meera Chand, director of clinical and emerging infections at UKHSA, said officials were looking at a wide range of possible factors which could be causing children to be admitted to hospital with liver inflammation.
"One of the possible causes that we are investigating is that this is linked to adenovirus infection. However, we are thoroughly investigating other potential causes," she said.
Common virus
Adenoviruses are a family of viruses that usually cause a range of mild illnesses such as colds, vomiting and diarrhoea.
Hepatitis is not a common complication of these viruses but in rare cases a link has been found.
Dr Chand said parents should supervise good handwashing and hygiene at home, as well as keeping an eye out for possible symptoms.
"We are calling on parents and guardians to be alert to the signs of hepatitis - including jaundice - and to contact a healthcare professional if they are concerned."
Other symptoms of the liver condition include dark urine, itchy skin, muscle pain and a loss of appetite.
The UKHSA says there is "no link" between these recent infant hepatitis cases and the Covid-19 vaccine, as none of the children involved has been been vaccinated.