The total Compton profile for the 110 direction of crystalline copper has been measured with high statistical accuracy by a -ray scattering experiment. Special attention was paid to the correction of multiple photon scattering in the sample and the slight spectral contamination of the incident radiation. The results are discussed in conjunction with earlier measurements of the Compton profile anisotropies and existing band-structure calculations. The effect of the electron correlation on the Compton profile and the momentum density is found to be significantly larger than in the homogeneous electron gas. A correlation correction functional required by the Hohenberg-Kohn-Sham density-functional theory is calculated in the local density approximation and is shown to improve the agreement between density-functional band-structure calculations and experiment. The remaining discrepancies can be characterized by a redistribution of momentum density in reciprocal space as compared to the model of noninteracting electrons. The appearance of this nonlocal correlation effect is specific for the momentum density and does not contradict the generally good agreement between one-electron theory and other experimental results for copper. Possible origins of the effect are discussed tentatively.