The phenomenon is being aggravated by overburdened health services where medical workers are being diverted from giving vaccines to focus on the COVID-19 response.
Some governments might even have to postpone mass immunisation campaigns as a way of slowing the disease's spread, UNICEF said.
The agency's Executive Director Henrietta Fore said the requirement for people to stay home and observe social distancing was leading parents to "make the difficult decision to defer routine immunisation".
Of particular concern are impoverished and war-torn countries battling measles, cholera or polio outbreaks, such as Afghanistan, the Democratic Republic of Congo, Somalia, the Philippines, Syria and South Sudan.
"At a time like this, these countries can ill-afford to face additional outbreaks of vaccine-preventable diseases," Fore said in a statement.
"Medical goods are in short supply and supply chains are under historic strain due to transport disruptions. Flight cancellations and trade restrictions by countries have severely constrained access to essential medicines, including vaccines."
Fore added that in the near future, governments may need to postpone preventive mass vaccination campaigns -- where people group together to receive inoculations -- to ensure these do not contribute to the spread of COVID-19.
UNICEF recommended governments begin rigorous planning now to boost immunisation campaigns for as soon as the coronavirus pandemic is under control.
Afghanistan is one of only three countries, along with Pakistan and Nigeria, where polio remains endemic.
Even before the coronavirus crisis, Afghanistan and neighbouring Pakistan were struggling to vaccinate kids as local populations viewed inoculation teams with suspicion.
Opposition grew after the CIA organised a fake vaccination drive to help track down Al-Qaeda's former leader Osama Bin Laden in the Pakistani city of Abbottabad.
The Taliban last week pledged to cooperate with healthcare workers in combatting the coronavirus.