Climate change, which leads to higher temperatures, droughts, and storms, is expected to have a strong effect on both health of forest trees and associated biodiversity. The aim of this study was to investigate the diversity and composition of fungal communities associated with the functional tissues and rhizosphere soil of healthy-looking Picea abies to better understand these fungal communities and their potential effect on tree health in the process of climate change. The study sites included 30 P. abies stands, where needles, shoots, roots, and the rhizosphere soil was sampled. DNA was isolated from individual samples, amplified using ITS2 rRNA as a marker and subjected to high-throughput sequencing. The sequence analysis showed the presence of 232,547 high-quality reads, which following clustering were found to represent 2701 non-singleton fungal OTUs. The highest absolute richness of fungal OTUs was in the soil (1895), then in the needles (1049) and shoots (1002), and the lowest was in the roots (641). The overall fungal community was composed of Ascomycota (58.3%), Basidiomycota (37.2%), Zygomycota (2.5%), Chytridiomycota (1.6%), and Glomeromycota (0.4%). The most common fungi based on sequence read abundance were Aspergillus pseudoglaucus (7.9%), Archaeorhizomyces sp. (3.6%), and Rhinocladiella sp. (2.0%). Pathogens were relatively rare, among which the most common were Phacidium lacerum (1.7%), Cyphellophora sessilis (1.4%), and Rhizosphaera kalkhoffii (1.4%). The results showed that the detected diversity of fungal OTUs was generally high, but their relative abundance varied greatly among different study sites, thereby highlighting the complexity of interactions among the host trees, fungi, and local environmental conditions.