The International Rescue Committee said the situation was on the verge of spiralling out of control, with widespread community transmission and inadequate health care.
It said the official figure of 835 confirmed cases was far from reality.
The group's comments echoes a statement from the mayor of Somalia's capital, Mogadishu, earlier this week. Omar Filish said the city had seen an unusual number of deaths recently and warned that the country was under-counting cases of coronavirus.
Somalia is already struggling with the worst locust invasion in 25 years, plus a drought and floods - as well as conflict.
More than five million people need humanitarian aid to survive in the country.
