The children have been forced to flee their homes following the overthrow of the government by a rebel alliance in March this year, the charity says.
Many of them are suffering from malnutrition and malaria.
Mark Kaye, a spokesman for the charity, told the BBC the health system had been almost completely destroyed.
The UN Security Council is due to discuss the crisis in the Central African Republic (CAR) on Wednesday.
Michel Djotodia, who seized power from President Francois Bozize when fighters from the Seleka rebel coalition marched into the capital, Bangui, on 24 March 2013, has promised to relinquish power after elections scheduled for 2016.
Earlier this month, UN chief Ban Ki-moon said there had been a “total breakdown of law and order” since the coup and infighting among rebel groups had led to widespread abuses.
‘Deserted villages’
Save the Children said many families were running out of food, and many were still hiding in the bush, afraid to return home.
Those children not the direct victims of violence had witnessed widespread looting and their parents being threatened or beaten, the charity said in a statement.
“What we’ve seen is an almost complete destruction of the existing health system. I’ve seen deserted villages,” Mr Kaye told the BBC World Service’s Newsroom programme.
The looting was not just of food reserves and people’s possessions, he said.
“All the pharmacies have been hit. There are no medications, no drugs, equipment has been stolen.
“I’ve been to hospitals where even the mattresses have been stolen.”
Mr Kaye said that aid organisations urgently needed help to avoid a humanitarian catastrophe.
“This isn’t just a forgotten crisis from the coup. This country has been largely ignored for the best part of a decade now.
“Even before this coup one in 10 children died before they reached the age of one and 15 out of 100 died before they reached the age of five.”
Over the weekend, Mr Ban urged the UN Security Council to consider sanctions or to set up a panel of experts to monitor the situation in CAR.
In April, regional states agreed to send 2,000 peacekeepers to bolster a 500-strong multinational force that was battling to help the interim government restore stability.
CAR, a former French colony, has an unstable history and is extremely poor, though it has large deposits of minerals including gold and diamonds.