The circular said pupils would have to say the verse after singing the national anthem at school assembly in the governorate of Amran.
The move was condemned by Muammar Al Eryani, Minister of Information at Yemen's internationally recognised government.
“This dangerous move falls under the Houthi militia’s agenda, which since the rebellion began, aims to deform children’s national and Arab identity and brainwash them with dark, extremist thoughts,” he said.
Mr Al Eryani said the chant rule was designed to “instill hatred to the other” and “obliterate the principles of tolerance among Yemenis”.
The move also drew criticism from Yemenis in the country and abroad.
“It’s shocking that millions of students will now have to chant violent death and hate speech as they wake up to school,” said Ibrahim Jalal, a Yemeni analyst and non-resident scholar at the Middle East Institute in Washington.
Mr Jalal told The National that the Houthi order would be "imposed using all available means".
"Those who try to opt out will face consequences. In fact, some already have, not to mention that pro-Houthi teachers have replaced a number of cadres, school headmasters and headmistresses," he said.
"The order normalises the idea of death in day-to-day discourse in the most life-appreciating institutions: schools."
A former Yemeni diplomat told The National that mandating the chant would only radicalise young children.
“This is very depressing. It hits the youngest generation,” he said.
The chant was first used by former Iranian supreme leader Ayatollah Ruhollah Khomeini and has since been heard in Afghanistan, Lebanon, Yemen and Pakistan.
The Iran-backed Houthis have put the full phrase on the group's official flag.
In 2018, Mr Al Eryani shared a video that showed armed Houthis forcing primary school pupils to recite the chant.
Several more videos were circulated in Yemen showing a similar scene.
Yemen is in its eighth year of war after the Houthis seized the capital Sanaa in 2014. A Saudi-led coalition intervened on behalf of the internationally recognised government.