Abdullaahi Hashi Ali, the ministry’s director general, told Anadolu Agency in an exclusive interview at least 407 people had lost their lives so far.
Almost 18,000 people were also receiving hospital treatment for illnesses, he added.
"The most affected regions by drought and cholera are Bay, Bakol, Middle Shabelle and Lower Shabelle. We have organized 60 medical mobile teams in order to overcome this deadly disease," he said.
Mustaf Mayow, director of Qasahdhere district hospital in the Bay region, told Anadolu Agency people were dying from cholera every day.
The Somali government, supported by UNICEF and the WHO, is fighting against waterborne diseases and earlier described a looming famine as a national disaster.
The current drought in Somalia is the worst since 1945, according to the UN.
Half the country's population is in need of emergency humanitarian assistance, including thousands of children.
On Tuesday, a Turkish Airlines aircraft carrying medical supplies and food aid arrived in the Somali capital, Mogadishu.