Coherent manipulation of matter waves, a distinctive hallmark of quantum mechanics, is fundamental to modern quantum technologies. Spatial adiabatic passage (SAP) is a prime example of this phenomenon, where a wave packet is transferred between two uncoupled localized modes by adjusting the tunneling coupling to an intermediate third mode in a counterintuitive sequence. Although this concept was introduced over two decades ago, its observation was previously limited to electromagnetic waves. In this study, we demonstrate this quantum interference effect using massive particles that tunnel between three micro-optical traps ("optical tweezers"). We begin by preparing ultracold fermionic atoms in low vibrational eigenstates of one trap, followed by manipulating the distance between the traps to execute the SAP protocol. We observe a smooth and high-efficiency transfer of atoms between the two outer traps, with a very low population remaining in the central trap. These findings open possibilities for advanced control schemes in optical tweezer array platforms.