"We are devastated that we are unable to continue to offer healthcare, nutritional support, child protection and education to the approximately 250,000 children and family members served by our current programmes," charity chief Mike Aaronson said on Tuesday.
"However, we just cannot continue to expose our staff to the unacceptable risks they face as they go about their humanitarian duties in Darfur," he added.
Two of the charity's workers were killed on 12 December in an attack the United Nations blamed on rebels fighting government forces in the region the size of France.
Two others were killed in October when their vehicle hit a landmine.
Tens of thousands of people have been killed, and some 1.8 million forced to flee in nearly two years of fighting.
The African Union (AU), which is trying to mediate, has warned the region is a ticking bomb with vast quantities of arms and ammunition flooding in.
Earlier this month, the head of British charity Oxfam was forced to quit Sudan after being accused of working under the wrong visa and meddling in politics.
Two of Save the Children's staff
were killed by rebels in Darfur
"This is not just about one agency deciding to leave. There is a real threat to the whole humanitarian operation at the moment," Aaronson later told BBC radio.
Sudan's parliament has approved a one-year extension of the five-year-old state of emergency amid ongoing security concerns, the official Suna news agency reported.
State of emergency
Security and defence committee chairman Muhammad Bakhit was quoted as saying that parliament had also passed on Monday President Umar al-Bashir's request for an extension, on the grounds that opposition groups were threatening the country's oil infrastructure in the north and east.
Parliament also renewed its own tenure, as well as those of several other government institutions.
Some members of the opposition had blasted al-Bashir's effort to renew the state of emergency as the "continuation of an anti-democracy policy".