Exosomal heat shock proteins (Hsps) are involved in intercellular communication both in physiological and pathological conditions. They play a role in key processes of carcinogenesis including immune system regulation, cell differentiation, vascular homeostasis and metastasis formation. Thus, exosomal Hsps are emerging biomarkers of malignancies and possible therapeutic targets. Adolescents and young adults (AYAs) are patients aged 15–39 years. This age group, placed between pediatric and adult oncology, pose a particular challenge for cancer management. New biomarkers of cancer growth and progression as well as prognostic factors are desperately needed in AYAs. In this review, we attempted to summarize the current knowledge on the role of exosomal Hsps in selected solid tumors characteristic for the AYA population and/or associated with poor prognosis in this age group. These included malignant melanoma, brain tumors, and breast, colorectal, thyroid, hepatocellular, lung and gynecological tract carcinomas. The studies on exosomal Hsps in these tumors are limited; however; some have provided promising results. Although further research is needed, there is potential for future clinical applications of exosomal Hsps in AYA cancers, both as novel biomarkers of disease presence, progression or relapse, or as therapeutic targets or tools for drug delivery.