The cases were respectively detected at Elegu town in the country's northern district of Amuru, bordering neighbouring South Sudan, Mayuge, a district in eastern Uganda, and Kawaala, a neighborhood within Kampala, the country's capital, Daniel Kyabayinze, director of public health in the Ministry of Health, told Xinhua news agency over the telephone.
He said the three patients are currently undergoing treatment at Entebbe National Isolation Centre, about 40 km south of Kampala.
"We have five cases so far in Uganda. Two (have) recovered and did not have secondary infections," said Kyabayinze.
Health personnel earlier this month detected two cases of monkeypox imported from the neighbouring Democratic Republic of the Congo (DRC) in Uganda's western district of Kasese.
The two positive cases were among six suspected infections in Mpondwe and Bwera, towns bordering the DRC, according to the Ministry of Health.
The World Health Organization (WHO) earlier this month declared monkeypox a public health emergency of international concern, sounding the alarm over its potential for further international transmission.
Mpox, also known as monkeypox, is an infectious disease caused by the monkeypox virus that is spread through close contact, including fever, swelling of the lymph nodes, sore throat, muscle aches, skin rash, and back pain.