Sweet potato (Ipomoea batatas L. Lam.) is a major source of food in many parts of Ethiopia. In recent years, viral diseases have become the main threat to sweet potato production in Ethiopia. Previous virus survey studies carried out from 1986 to 2020 reported eight viruses infecting sweet potato in Ethiopia. Consequently, obtaining and multiplying virus-free planting materials have been difficult for farmers and commercial multipliers. This study was conducted to detect viruses infecting the five sweet potato varieties used as source plants and compare the virus elimination efficiency between meristem cultures from untreated and heat-treated mother plants and production of virus-free sweet-potato-planting materials. Seven common viruses were tested for, using grafting to Ipomoea setosa, enzyme-linked immunosorbent assay (ELISA) and reverse-transcription polymerase chain reaction (RT–PCR) before and after elimination procedures as screening and confirmatory methods. The sweet potato feathery mottle virus (SPFMV) elimination efficiencies of meristem cultures from untreated (grown at 25 ± 1 °C) and heat-treated (grown at 39 ± 1 °C) potted plants of sweet potato varieties were evaluated and compared. Sweet potato feathery mottle virus (SPFMV) was detected in 12 of the 15 source plants tested. Triple infections of SPFMV, sweet potato chlorotic stunt virus (SPCSV), and sweet potato virus C (SPVC) were detected in one of the fifteen plants. This study reports the detection of SPVC for the first time in sweet potato plants from Ethiopia. The cutting of meristems from heat-treated plants further increased the percentage of virus-free plantlets by ca 10% to ca 16%, depending on the plant variety. Elimination efficiency also seemed to vary among varieties: the greatest difference was observed for ‘Tola’, and the least difference was observed for ‘Guntute’. The present study provided protocols for detecting viruses and generating virus-free sweet-potato-planting materials in Ethiopia.