Knowledge of the composition of proteins that interact with plasma DNA will provide a better understanding of the homeostasis of circulating nucleic acids and the various modes of interaction with target cells, which may be useful in the development of gene targeted therapy approaches. The goal of the present study is to shed light on the composition and architecture of histone-containing nucleoprotein complexes (NPCs) from the blood plasma of healthy females (HFs) and breast cancer patients (BCPs) and to explore the relationship of proteins with crucial steps of tumor progression: epithelial–mesenchymal transition (EMT), cell proliferation, invasion, cell migration, stimulation of angiogenesis, and immune response. MALDI-TOF mass spectrometric analysis of NPCs isolated from blood samples using affine chromatography was performed. Bioinformatics analysis showed that the shares of DNA-binding proteins in the compositions of NPCs in normal and cancer patients are comparable and amount to 40% and 33%, respectively; in total, we identified 38 types of DNA-binding motifs. Functional enrichment analysis using FunRich 3.13 showed that, in BCP blood, the share of DNA-binding proteins involved in nucleic acid metabolism increased, while the proportion of proteins involved in intercellular communication and signal transduction decreased. The representation of NPC passenger proteins in breast cancer also changes: the proportion of proteins involved in transport increases and the share of proteins involved in energy biological pathways decreases. Moreover, in the HF blood, proteins involved in the processes of apoptosis were more represented in the composition of NPCs and in the BCP blood—in the processes of active secretion. For the first time, bioinformatics approaches were used to visualize the architecture of circulating NPCs in the blood and to show that breast cancer has an increased representation of passenger proteins involved in EMT, cell proliferation, invasion, cell migration, and immune response. Using breast cancer protein data from the Human Protein Atlas (HPA) and DEPC, we found that 86% of NPC proteins in the blood of BCPs were not previously annotated in these databases. The obtained data may indirectly indicate directed protein sorting in NPCs, which, along with extracellular vesicles, can not only be diagnostically significant molecules for liquid biopsy, but can also carry out the directed transfer of genetic material from donor cells to recipient cells.