The first major outbreak in two years forced the southern African country to suspend all beef exports on August 24.
Annually it exports about 9,000 tons of beef to the EU.
Assistant minister of agriculture Molebatsi Molebatsi told AFP that 9,757 cattle are expected to be culled in northeastern villages bordering its neighbor, Zimbabwe.
He warned that numbers of infected cattle "keep on increasing".
There are some 19,000 in the affected region, he said.
After a two year respite, in August the landlocked Southern African nation confirmed an outbreak.
Foot and mouth disease is a severe, highly contagious viral disease of livestock.
Botswana exports about 9,000 tonnes of beef to the EU each year -- around half of its exports -- competing with world renowned beef producers such as Brazil.
The deal enables Botswana to export duty free and quota free to the EU market.