The charity said floods in Nigeria, Mali, Niger and the Democratic Republic of Congo had driven nearly one million people from their homes.
"The unprecedented rains... have created a worsening education crisis with the damage or destruction of schools, the occupation of school buildings by displaced families, and the displacement of families away from schools," Save the Children said in a statement.
"These kinds of extreme weather events are becoming more frequent and severe as a result of the climate crisis," it added.
Save the Children called on governments to urgently offer alternatives to children missing out on education and ensure that schools were more resilient to future extreme weather events.
It also urged its donors to support scaling up assistance for the affected populations.
The 10 million children stuck at home or displaced are in addition to around 36 million estimated to be out of school due to conflict and poverty in the four countries, Save the Children said, citing UNESCO figures.
More than 20 million of these children are in Nigeria, Africa's most populous country, it added.
"As well as seeing their families devastated and their homes destroyed, the children have to come to terms with witnessing the flooding of their education," Vishna Shah-Little, Save the Children's regional director of advocacy and campaigns said in the statement.
Torrential downpours since the start of the rainy season have triggered flooding that has killed hundreds and displaced hundreds of thousands across Chad, Nigeria, Burkina Faso, Mali, Niger, Guinea and Cameroon.
The floods have also caused significant damage to infrastructure and land, as well as increasing the risk of disease and food insecurity.
Save the Children called on national governments to rapidly phase out the use and subsidy of fossil fuels as part of the global response to climate change.
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