The formation of aggregates by misfolded proteins is thought to be inherently toxic, affecting cell fitness. This observation has led to the suggestion that selection against protein aggregation might be a major constraint on protein evolution. The precise fitness cost associated with protein aggregation has been traditionally difficult to evaluate. Moreover, it is not known if the detrimental effect of aggregates on cell physiology is generic or depends on the specific structural features of the protein deposit. In bacteria, the accumulation of intracellular protein aggregates reduces cell reproductive ability, promoting cellular aging. Here, we exploit the cell division defects promoted by the intracellular aggregation of Alzheimer's-disease-related amyloid β peptide in bacteria to demonstrate that the fitness cost associated with protein misfolding and aggregation is connected to the protein sequence, which controls both the in vivo aggregation rates and the conformational properties of the aggregates. We also show that the deleterious impact of protein aggregation on bacterial division can be buffered by molecular chaperones, likely broadening the sequential space on which natural selection can act. Overall, the results in the present work have potential implications for the evolution of proteins and provide a robust system to experimentally model and quantify the impact of protein aggregation on cell fitness.