Prototypical three-dimensional (3D) topological Dirac semimetals (DSMs), such as Cd3As2 and Na3Bi, contain electrons that obey a linear momentum-energy dispersion with different Fermi velocities along the three orthogonal momentum dimensions. Despite being extensively studied in recent years, the inherent Fermi velocity anisotropy has often been neglected in the theoretical and numerical studies of 3D DSMs. Although this omission does not qualitatively alter the physics of light-driven massless quasiparticles in 3D DSMs, it does quantitatively change the optical coefficients which can lead to nontrivial implications in terms of nanophotonics and plasmonics applications. Here we study the linear optical response of 3D DSMs for general Fermi velocity values along each direction. Although the signature conductivity-frequency scaling, σ(ω) ∝ ω, of 3D Dirac fermion is well-protected from the Fermi velocity anisotropy, the linear optical response exhibits strong linear dichroism as captured by the universal extinction ratio scaling law, Λij = (vi /vj )2 (where i ≠ j denotes the three spatial coordinates x,y,z, and vi is the i-direction Fermi velocity), which is independent of frequency, temperature, doping, and carrier scattering lifetime. For Cd3As2 and Na3Bi3, an exceptionally strong extinction ratio larger than 15 and covering a broad terahertz window is revealed. Our findings shed new light on the role of Fermi velocity anisotropy in the optical response of Dirac semimetals and open up novel polarization-sensitive functionalities, such as photodetection and light modulation.