The ferromagnet/oxide interface is key to developing emerging multiferroic and spintronic technologies with new functionality. Here we probe the Fe/MgO interface magnetization, and identify a new exchange bias phenomenon manifested only in the interface spin system, and not in the bulk. The interface magnetization exhibits a pronounced exchange bias, and the hysteresis loop is shifted entirely to one side of the zero field axis. However, the bulk magnetization does not, in marked contrast to typical systems where exchange bias is manifested in the net magnetization. This reveals the existence of an antiferromagnetic exchange pinning layer at the interface, identified here as FeO patches that exist even for a nominally 'clean' interface. These results demonstrate that atomic moments at the interface are non-collinear with the bulk magnetization, and therefore may affect the net anisotropy or serve as spin scattering sites. We control the exchange bias magnitude by varying the interface oxygen concentration and Fe-O bonding.