The structure of a neutron-rich ^{25}F nucleus is investigated by a quasifree (p,2p) knockout reaction at 270A MeV in inverse kinematics. The sum of spectroscopic factors of π0d_{5/2} orbital is found to be 1.0±0.3. However, the spectroscopic factor with residual ^{24}O nucleus being in the ground state is found to be only 0.36±0.13, while those in the excited state is 0.65±0.25. The result shows that the ^{24}O core of ^{25}F nucleus significantly differs from a free ^{24}O nucleus, and the core consists of ∼35% ^{24}O_{g.s.}. and ∼65% excited ^{24}O. The result may infer that the addition of the 0d_{5/2} proton considerably changes neutron structure in ^{25}F from that in ^{24}O, which could be a possible mechanism responsible for the oxygen dripline anomaly.