We present simultaneous two-dimensional spectroscopy of the circumnuclear region (12" x 9") of the galaxy NGC 7331, obtained with an optical fiber system coupled to the ISIS double spectrograph of the 4.2 m William Herschel Telescope. The system allows simultaneous observation of 125 regions of this galaxy in two spectral ranges: 4590--5400 Angstroms at high resolution (1.5 Angstroms) and 6400--9620 Angstroms at low resolution (5 Angstroms). These spectra are mainly used to study the stellar and gas kinematics in the innermost region of this galaxy. The stellar velocity fields inferred from the Mg I b and Ca II absorption lines are in good agreement. They show a solid-body rotational pattern with the line of nodes along the position angle of the apparent major axis of the galaxy. The relatively large local stellar velocity dispersion suggests that we are observing the bulge rather than the disk kinematics. The two-dimensional kinematic data agree with previous one-dimensional studies that found no evidence for a massive black hole in NGC 7331. The [O III] emission lines are split into three components. One is distributed around the systemic velocity, another is systematically blueshifted, and the last is systematically redshifted. We propose that these arise from two distinct gaseous systems: a warped disk of irregular rotational pattern with the kinematic axes shifted by about 30 deg with respect to those of the stars, and a shell of gas flowing radially. Although alternative interpretations in terms of inflow driven by a central bar or outflow produced by a galactic wind are possible, the latter seems preferable. In NGC 7331 the ionized gas and stars are kinematically decoupled, the velocity dispersion of the ionized gas being substantially lower than that of the stars. This last result differs from what is generally found in Seyfert galaxies. However, NGC 7331 and M31 show a large degree of similarity, and the type of LINERs that they harbor are probably produced by the same type of phenomenon.