The advert, which was broadcast on television only after 9pm, began with a warning message saying that it would show a real birth scene, which viewers might find distressing.
It showed a woman giving birth to an apparently lifeless baby with the help of a midwife.
On-screen text then said: "For a million newborns every year, their first day is also their last."
The midwife was then shown administering care to the baby, who began crying.
Further on-screen text then said: "Basic training for midwives can help end first-day deaths." This was followed by an invitation to make a £5 text donation to the charity.
The advert attracted 614 complaints, most of which said that the images of live childbirth were offensive, overly graphic and unduly shocking and distressing.
Complainants also said the advert would cause undue distress and offence to people who had lost a child through miscarriage or stillbirth. Others said it was demeaning and exploited the mother.
Save the Children told the ASA the advert was meant to illustrate that a million babies die on the day they are born. It said it believed the images of childbirth were not offensive and the warning message gave people enough time to choose whether or not they watched.
The charity said the advert did not undermine the mother’s dignity and had been filmed with her consent and her full knowledge of how it would be used.
The ASA’s ruling, published today, did not uphold any of the complaints and ruled that although some people might find the advert offensive it was "unlikely to cause serious or widespread offence".
It said that the advert "communicated the issue of death during childbirth in a manner that respected the dignity of the mother while raising awareness of that issue".
The watchdog said the post-9pm restriction on the advert meant it was less likely to be seen by children and it "considered the scheduling of the ads reduced the risk of the ads causing distress to young viewers".
A spokeswoman for Save the Children said it did not intend to upset anyone but simply to raise awareness of the fact that a million babies die every year on the day they are born.
"We accept that the content is shocking, which is why we included an advisory warning before it was shown," she said. "The death of every baby is a tragedy. By showing this advert, Save the Children hopes to bring to the attention of the world the scandal of first-day deaths and encourage members of the public to support our call to tackle it."