Antiferromagnets (AFMs) have the potential to push spintronic devices from a static condition or gigahertz frequency range to the terahertz range for the sake of high-speed processing. However, the insensitivity of AFMs to magnetic fields makes the manipulation of spin currents difficult. The ultrafast generation of the spin current in ferromagnet/heavy-metal (HM) structures has received a lot of attention in recent years, but whether a similar scenario can be observed in an AFM/HM system is still unknown. Here, we show the optical generation of ultrafast spin current in an AFM/HM heterostructure at zero external magnetic field and at room temperature by detecting the associated terahertz emission. We believe that this is a common phenomenon in antiferromagnets with strong nonlinear optical effects. Our results open an avenue of fundamental research into antiferromagnetism and a route to AFM spintronic devices. Spin currents are generated from an antiferromagnet/heavy-metal heterostructure using optical excitation on picosecond timescales. This will have applications in antiferromagnetic spintronics.