The missile struck a mosque at the al-Estiqbal camp in Marib where soldiers had gathered for evening prayers.
The government blamed the rebel Houthi movement, but it did not immediately confirm it had launched the missile.
It was one of the bloodiest single attacks since the conflict in Yemen escalated five years ago.
The fighting between the Houthis and forces loyal to the government, which is backed by a Saudi-led coalition, has devastated the country, killed an estimated 100,000 people, and triggered the world’s worst humanitarian crisis.
More than 11 million people face a daily struggle to find enough food, and 240,000 people live in famine-like conditions, according to the World Food Programme.
Initial reports about the attack on al-Estiqbal camp, which is 170km (105 miles) east of the rebel-held capital Sanaa, said at least 80 soldiers were killed.
But by Sunday night the death toll had risen to at least 111 due to the “serious and fatal injuries sustained by the soldiers”, Health Ministry Undersecretary Abdul Raqeeb al-Haidari told the news website al-Masdar Online.
Military and medical sources told AFP news agency that 116 people had died.
President Abdrabbuh Mansour Hadi denounced the missile attack as a “cowardly and terrorist” act, which he said confirmed “without doubt that the Houthis have no desire for peace”.
The Saudi foreign ministry said the incident “reflects this terrorist militia’s disregard for sacred places and… for Yemeni blood”.
The United Nations special envoy for Yemen, Martin Griffiths, condemned the recent escalation of hostilities in the country, and said Saturday’s attack was “of particular concern”.
“I have said before that the hard-earned progress that Yemen has made on de-escalation is very fragile. Such actions can derail this progress,” he warned. “I urge all parties to stop the escalation now and to direct their energy away from the military front and into the politics.”