The attack happened on Sunday at the village of Ngalewa, near the border with Nigeria, the governor of Diffa region, Laouali Mahamane Dan Dano, told state TV.
"Boko Haram elements ... slit the throats of nine people... they took women, 37 women, and departed with them," he said.
"The defence and security forces are already in pursuit, and we hope that in the coming days these women will be found and freed," he said.
The governor, who went to Ngalewa on Monday, said the village had been singled out because it was known for its resistance to the jihadists.
The assailants came by foot for greater stealth, he said.
The village's mayor, Abari El Hadj Daouda, told AFP by phone that the attack happened on Sunday evening, "between 10 and 11pm."
"About 30 or 40 women and children were kidnapped... (and) nine people killed," he said.
The village lies a few kilometres (miles) north of the town of Kabalewa, where there was a suicide attack last Wednesday.
Diffa, which as a population of around 600,000 people, has suffered a string of attacks by the Nigeria-based Boko Haram since 2015.
Around 300,000 people displaced by jihadist attacks have taken refuge in the region, which already grapples with grinding poverty.
In April 2014, Islamist militants seized 276 schoolgirls from the remote northeast Nigerian town of Chibok, triggering global condemnation and drawing attention to the bloody Boko Haram insurgency.
Fifty-seven escaped in the immediate aftermath. Of the 219 who did not manage to flee, 106 have either been released or found, leaving 113 still missing.
The attack on Sunday coincided with a visit to Niger's western neighbour Mali by French President Emmanuel Macron, aimed at boosting multinational efforts to fight jihadism in countries south of the Sahara.
The so-called G5 Sahel nations Burkina Faso, Chad, Mali, Mauritania and Niger, plan to set up a regional force.
