Antiferromagnetic (AFM) spintronics has emerged as a subfield of spintronics driven by the advantages of antiferromagnets producing no stray fields and exhibiting ultrafast magnetization dynamics. The efficient method to detect an AFM order parameter, known as the Néel vector, by electric means is critical to realize concepts of AFM spintronics. Here, we demonstrate that noncollinear AFM metals, such as Mn_{3}Sn, exhibit a momentum dependent spin polarization which can be exploited in AFM tunnel junctions to detect the Néel vector. Using first-principles calculations, we predict a tunneling magnetoresistance (TMR) effect as high as 300% in AFM tunnel junctions with Mn_{3}Sn electrodes, where the junction resistance depends on the relative orientation of their Néel vectors and exhibits four nonvolatile resistance states. We argue that the spin-split band structure and the related TMR effect can also be realized in other noncollinear AFM metals like Mn_{3}Ge, Mn_{3}Ga, Mn_{3}Pt, and Mn_{3}GaN. Our work provides a robust method for detecting the Néel vector in noncollinear antiferromagnets via the TMR effect, which may be useful for their application in AFM spintronic devices.