Exosomes are directly involved in governing of physiological and pathological conditions of an organism through the transfer of information from producing to receiving cells. It can be assumed that exosomes are one of the key players of tumor dissemination since they are very stable and small enough to penetrate from various tissues into biological fluids and then back, thus interacting with tissue target cells. We evaluated the enzymatic activity and the level of 20S proteasome in tissue and exosomes of healthy females (n = 39) and patients with ovarian (n = 50) and breast (n = 108) tumors to reveal the critical role of exosomal cargo in the mediation of different types of metastases. Exosomes from plasma and ascites were isolated and characterized in according to International Society for Extracellular Vesicles guidelines. The level of 20S proteasome in tissue and exosomes was determined using Western blot analysis. Chymotrypsin- and caspase-like (ChTL and CL, respectively) peptidase activities of the proteasomes were determined using fluorogenic Suc-LLVY-AMC and Cbz-LLG-AMC substrates, respectively. We observed increased levels of 20S proteasome in ovarian cancer tissue and luminal B subtype breast cancer tissue as well as in plasma exosomes from cancer patients. Moreover, the level of the 20S proteasome in plasma exosomes and ascites exosomes in patients with ovarian tumors is comparable and higher in ovarian cancer patients with low volume ascites than in patients with moderate and high-volume ascites. We also found increased ChTL and CL activities in breast cancer and ovarian cancer tissues, as well as in peritoneal metastases in ovarian cancer, while proteasomal activity in exosomes from plasma of healthy females and all patients, as well as from ascites of ovarian tumor patients were lower than detection limit of assay. Thus, regardless of the type of tumor metastasis (lymphogenous or peritoneal), the exosomes of cancer patients were characterized by an increased level of 20S proteasome, which do not exhibit enzymatic activity.