The molecular mechanisms by which polyglutamine (polyQ)-expanded huntingtin (Htt) causes neurodegeneration in Huntington’s disease (HD) remain unclear. The malfunction of cellular proteostasis has been suggested as central in HD pathogenesis and also as a target of therapeutic interventions for the treatment of HD. We present results that offer a previously unexplored perspective regarding impaired proteostasis in HD. We find that, under non-stress conditions, the proteostatic capacity of cells expressing full length polyQ-expanded Htt is adequate. Yet, under stress conditions, the presence of polyQ-expanded Htt impairs the heat shock response, a key component of cellular proteostasis. This impaired heat shock response results in a reduced capacity to withstand the damage caused by cellular stress. We demonstrate that in cells expressing polyQ-expanded Htt the levels of heat shock transcription factor 1 (HSF1) are reduced, and, as a consequence, these cells have an impaired a heat shock response. Also, we found reduced HSF1 and HSP70 levels in the striata of HD knock-in mice when compared to wild-type mice. Our results suggests that full length, non-aggregated polyQ-expanded Htt blocks the effective induction of the heat shock response under stress conditions and may thus trigger the accumulation of cellular damage during the course of HD pathogenesis.