The charity said medics across northwest Syria were looking to fortify hospitals after a wave of attacks in rebel-held east Aleppo left facilities struggling to care for injured children.
Regime forces have been waging a ferocious assault on east Aleppo since November 15, with the Syrian Observatory for Human Rights saying more than 140 civilians have been killed, 19 of them children.
The renewed fighting comes amid international concern for the fate of more than 250,000 civilians trapped in besieged rebel-held areas of the northern city.
Save the Children also condemned a rebel attack on west Aleppo that killed at least eight children on Sunday.
It said among those killed at the weekend was an education worker at a school it supports in east Aleppo who was found buried in rubble along with her baby son.
Classes at 13 such schools in east Aleppo had been suspended as shelling intensified in recent days, said Save the Children.
It said the deadly rebel attack on the school in the west of the city showed "there is no safe place for children in this conflict".
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"Children and aid workers are being bombarded by missiles whilst they are sitting at their desks in schools and seeking treatment in hospitals which are also under attack," said Sonia Khush, Syria director for Save the Children.
"The very places they should feel safest have become deadly," she said.
"It is a moral outrage that the death toll of Aleppo's children continues to grow and seems only set to get worse, whilst so little action is being taken to end the bombing and hold warring parties accountable for these attacks on civilians."
Save the Children called for an internationally monitored ceasefire to bring humanitarian relief into east Aleppo and evacuate the sick and wounded
It said the United Nations and opposition groups had already agreed on access for an aid convoy which could go ahead once all sides agree to a ceasefire.
"Parties to the conflict must come together to agree an immediate ceasefire, and to evacuate civilian casualties and get life-saving aid into the area."
UN Syria envoy Staffan de Mistura was rebuffed in Damascus on Sunday on a truce proposal that would allow the opposition to administer the city's east.
Aleppo was once the country's economic powerhouse, but it has been ravaged by the brutal war across Syria that has killed 300,000 people since it began with anti-government protests in March 2011.