We herein report a water-stable three-dimensional Cu-based metal-organic framework (MOF) 1 supported by a tritopic quaternized carboxylate and 4,4'-dipyridyl sulfide as an ancillary ligand. This MOF exhibits unique pore shapes with aromatic rings, positively charged pyridinium and unsaturated Cu(II) cation centers, free carboxylates, tessellating H2O, and coordinating SO4(2-) on the pore surface. Compound 1 can interact with two carboxyfluorescein (FAM)-labeled single-stranded DNA sequences (probe ss-DNA, delineated as P-DNA) through electrostatic, π-stacking, and/or hydrogen-bonding interactions to form two P-DNA@1 systems, and thus quench the fluorescence of FAM via a photoinduced electron-transfer process. These P-DNA@1 systems can be used as effective fluorescent sensors for human immunodeficiency virus 1 double-stranded DNA and Sudan virus RNA sequences, respectively, with detection limits of 196 and 73 pM, respectively.