Analysis of biomolecules at the single-molecule level is a great challenge in molecular diagnostics, gene profiling, and environmental monitoring. In this work, we design a smart plasmonic nanobiosensor based on individual Au@Ag core-shell nanocube (Au@Ag NC) modified with tetrahedron-structured DNA (tsDNA) for detecting microRNA 21 (miR-21) at the single-molecule level. An average localized surface plasmon resonance (LSPR) scattering spectral wavelength shift of approximately 0.4 nm can be obtained for a single miR-21 hybridization event on the nanobiosensor. In addition, the sensing mechanism of the individual Au@Ag NC is further verified by the three-dimensional finite-difference time-domain (3D-FDTD) simulations. Notably, this system not only allows the real-time detection of miR-21 with an aM level sensitivity over a large dynamic range from 1 aM to 1 nM, but also enables DNA-based logic operations as well as biomemory by exploiting miR-21, KpnI, and StuI-responsive assays. Our study opens a unique method for single-molecule detection of biomolecules and thus holds great promise in a variety of biological and biomedical applications.