Post-COVID-19 syndrome is a complex of different symptoms, which results in a multisystemic impairment after the suffering from COVID-19 infection. The aim of the study was to reveal the clinical, laboratory, and gut disorders in patients with post-COVID-19 syndrome (n = 39) before and after taking part in the 14-day complex program of rehabilitation. A complete blood count, coagulation test, blood chemistry, biomarkers, and metabolites in serum samples, and gut dysbiosis were revealed in patients on the day of admission and after 14-day rehabilitation, in comparison with the variables of healthy volunteers (n = 48) or with reference ranges. On the day of discharge, patients noted an improvement in respiratory function, general well-being, and mood. At the same time, the levels of some metabolic (4-hydroxybenzoic, succinic, fumaric acids) and inflammatory (interleukin-6) variables, which were increased on admission, did not reach the level of healthy people during the rehabilitation program. Taxonomy disbalance was observed in patients’ feces, namely, a high level of total bacterial mass, a decrease in the number of Lactobacillus spp., and an increase in pro-inflammatory microorganisms. The authors suggest that the post-COVID-19 rehabilitation program should be personalized, considering the patient’s state together with not only the baseline levels of biomarkers, but also with the individual taxonomy of the gut microbiota.