It said the two staff members were caught up in the attack in Kayah state as they were traveling back to their office after conducting humanitarian activities in a nearby community.
"Violence against innocent civilians including aid workers is intolerable, and this senseless attack is a breach of International Humanitarian Law," the group's chief executive, Inger Ashing, said in a statement.
"This is not an isolated event. The people of Myanmar continue to be targeted with increasing violence and these events demand an immediate response," Ashing said.
The army seized power in February, ousting the elected government and arresting top officials.
Its action was met by nonviolent nationwide demonstrations, which security forces quashed with deadly force, killing nearly 1400 civilians, according to the Assistance Association for Political Prisoners.
Peaceful protests have continued, but an armed resistance has also grown amid the severe crackdown, to the point that UN experts have warned the country could be sliding into civil war.
Save the Children called on the UN Security Council to respond to the army violence with steps including an arms embargo.
It also urged the Association of Southeast Asian Nations to press for the implementation of an agreement reached in April with Myanmar's leader calling for the cessation of violence in the country and mediation by an ASEAN special envoy.
Photos of the attack have spread on social media in Myanmar, fueling outrage against the military.
The photos show the charred bodies of over 30 people in three burned-out vehicles who were reportedly shot by government troops as they were fleeing combat.
On Sunday, the US Embassy in Myanmar said it was appalled by the "barbaric attack in Kayah state that killed at least 35 civilians, including women and children."
"We will continue to press for accountability for the perpetrators of the ongoing campaign of violence against the people of Burma," it said, using Myanmar's previous name.
Save the Children said it has been working in Myanmar since 1995, providing healthcare, food, education and child protection services. It said it has suspended operations in the region of the attack.
