The organisation warned on Tuesday in Geneva that, among other things, samples of the highly dangerous Ebola virus were stored there.
Patrick Youssef, the International Committee of the Red Cross' regional director for Africa, said that the laboratory - which is run by the National Institute for Biomedical Research - was at risk of power cuts.
The laboratory is located near the ICRC's office in Goma.
It is imperative that the virus does not escape from the laboratory, Youssef said.
Ebola is a contagious and life-threatening infectious disease.
The virus is transmitted through physical contact and contact with bodily fluids.
There have been repeated outbreaks in DR Congo and other countries in central and east Africa.
In 2014-15, more than 11,000 people died in an outbreak in west Africa.
According to Germany's Robert Koch Institute, mortality rates can be as high as 90 per cent if infected people are not treated immediately.
Rebels and the army are fighting in Goma, and hundreds of thousands of people have been displaced.
The World Health Organisation is warning of cholera outbreaks because people have no access to clean drinking water and sanitation is inadequate.
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