Of worldwide economic importance, Tomato yellow leaf curl virus (TYLCV, Begomovirus) is responsible for one of the most devastating plant diseases in warm and temperate regions. The DNA begomoviruses (Geminiviridae) are transmitted by the whitefly species complex Bemisia tabaci. Although geminiviruses have long been described as circulative non-propagative viruses, observations such as long persistence of TYLCV in B. tabaci raised the question of their possible replication in the vector. We monitored two major TYLCV strains, Mild (Mld) and Israel (IL), in the invasive B. tabaci Middle East-Asia Minor 1 cryptic species, during and after the viral acquisition, within two timeframes (0–144 hours or 0–20 days). TYLCV DNA was quantified using real-time PCR, and the complementary DNA strand of TYLCV involved in viral replication was specifically quantified using anchored real-time PCR. The DNA of both TYLCV strains accumulated exponentially during acquisition but remained stable after viral acquisition had stopped. Neither replication nor vertical transmission were observed. In conclusion, our quantification of the viral loads and complementary strands of both Mld and IL strains of TYLCV in B. tabaci point to an efficient accumulation and preservation mechanism, rather than to a dynamic equilibrium between replication and degradation.