Seed transmission can be of considerable relevance to the dissemination of plant viruses in nature and for their prevalence and perpetuation. Long-distance spread of isolates of the begomovirus species Tomato leaf curl New Delhi virus (genus Begomovirus, family Geminiviridae) has recently occurred from Asia to the Middle East and the Mediterranean Basin. Here, we investigated the possible transmission by melon (Cucumis melo L.) seeds of a tomato leaf curl New Delhi virus (ToLCNDV) isolate of the “Spain” strain widely distributed in the Mediterranean area as an alternative mechanism for long-distance spread. PCR amplification detection of ToLCNDV in floral parts and mature seeds of melon plants reveals that this virus is seedborne. “Seedborne” is defined as the ability of a virus to be carried through seeds, which does not necessarily lead to transmission to the next generation. Treatment with a chemical disinfectant significantly reduced the detectable virus associated with melon seeds, suggesting ToLCNDV contamination of the external portion of the seed coat. Also, when the internal fraction of the mature seed (seed cotyledons + embryo) was analyzed by quantitative PCR amplification, ToLCNDV was detectable at low levels, suggesting the potential for viral contamination or infection of the internal portions of seed. However, grow-out studies conducted with melon progeny plants germinated from mature seeds collected from ToLCNDV-infected plants and evaluated at early (1-leaf) or at late (20-leaf) growth stages did not support the transmission of ToLCNDV from seeds to offspring.