3′-Azidothymidine (AZT) reacts with 1-propargyl-5-R-1H- and 2-propargyl-5-R-2H-tetrazoles (R = H, Me, CH₂COOEt, CH₂CON(CH₃)₂, Ph, 2-CH₃-C₆H₄, or 4-NO₂-C₆H₄) via the Cu(I)-catalyzed asymmetric [3 + 2] cycloaddition to give 3′-modified thymidine analogs incorporating 1H-1,2,3-triazolyl, 1H-, and 2H-tetrazolyl fragments in 41–76% yield. The structures of the obtained compounds have been elucidated by means of HRESI⁺-MS, ¹H and ¹³C{¹H} NMR, and single crystal X-ray diffraction {for 3′-[4-(1H-5-N,N-dimethylaminocarbonylmethyltetrazol-1-yl)-1H-1,2,3-triazol-1-yl]thymidine 10d}. In vitro biological evaluation of the prepared compounds has been performed; they have exhibited low activity against phenotypic HIV-1_899A. Moderate anti-influenza activity against influenza virus A/Puerto Rico/8/34 (H1N1) strain has been observed in the cases of 3′-(4-(1H-tetrazol-1-ylmethyl)-1H-1,2,3-triazol-1-yl)thymidine 10a (IC₅₀ 39.6 μg/mL), 3′-(4-(2H-5-ethoxycarbonyltetrazol-2-ylmethyl)-1H-1,2,3-triazol-1-yl)thymidine 11c (IC₅₀ 31.6 μg/mL), and 3′-(4-(2H-5-(4-nitrophenyl)-tetrazol-2-ylmethyl)-1H-1,2,3-triazol-1-yl)thymidine 11g (IC₅₀ 46.4 μg/mL). The tested compounds possess very low cytotoxicity towards MDCK and MT4 cells as well as tumor human cervical carcinoma HeLa and promyelocytic leukemia HL-60 cells.