Certain Gram-negative bacteria use the type VI secretion system (T6SS) to kill and lyse competing bacteria. Here, we show that the T6SS-dependent lysis of prey cells by the naturally competent Acinetobacter baylyi results in the extensive filamentation of a subpopulation of A. baylyi cells. Filamentation is dependent on the release of DNA from the prey and its uptake by the competence system. The analysis of A. baylyi transcriptome and the response of transcriptional reporters suggest that the uptake of DNA results in the upregulation of the SOS response, which often leads to cell-division arrest. Long-term competition between competent and non-competent strains shows that the strain lacking the DNA uptake machinery outcompetes the parental strain only in the presence of the T6SS-dependent lysis of prey cells. Our data suggest that the cost of the induced SOS response may drive the selection of tight regulation or the loss of DNA uptake in bacteria capable of lysing their competitors.