Aims. Our goal was to investigate the molecular gas distribution and kinematics in the extreme far-infrared (FIR) excess galaxy NGC 1377 and to address the nature and evolutionary status of the buried source. Methods. We used high-(0.'' 65 x 0.'' 52, (65 x 52 pc)) and low-(4.'' 88 x 2.'' 93) resolution SubMillimeter Array (SMA) observations to image the (CO)-C-12 and (CO)-C-13 2-1 line emission. Results. We find bright, complex (CO)-C-12 2-1 line emission in the inner 400 pc of NGC 1377. The (CO)-C-12 2-1 line has wings that are tracing a kinematical component that appears to be perpendicular to the component traced by the line core. Together with an intriguing X-shape of the integrated intensity and dispersion maps, this suggests that the molecular emission of NGC 1377 consists of a disk-outflow system. Lower limits to the molecular mass and outflow rate are M-out(H-2) > 1 x 10(7) M-circle dot and (M) over dot > 8 M-circle dot yr(-1). The age of the proposed outflow is estimated to be 1.4 Myr, the extent to be 200 pc and the outflow speed to be V-out = 140 km s(-1). The total molecular mass in the SMA map is estimated to M-tot(H-2) = 1.5 x 10(8) M-circle dot (on a scale of 400 pc) while in the inner r = 29 pc the molecular mass is M-core(H-2) = 1.7 x 10(7) M-circle dot with a corresponding H-2 column density of N(H-2) = 3.4 x 10(23) cm(-2) and an average (CO)-C-12 2-1 brightness temperature of 19 K. (CO)-C-13 2-1 emission is found at a factor 10 fainter than (CO)-C-12 in the low-resolution map while (CO)-O-18 2-1 remains undetected. We find weak 1 mm continuum emission of 2.4 mJy with spatial extent less than 400 pc. Conclusions. Observing the molecular properties of the FIR-excess galaxy NGC 1377 allows us to probe the early stages of nuclear activity and the onset of feedback in active galaxies. The age of the outflow supports the notion that the current nuclear activity is young - a few Myr. The outflow may be powered by radiation pressure from a compact, dust enshrouded nucleus, but other driving mechanisms are possible. The buried source may be an active galactic nucleus (AGN) or an extremely young (1 Myr) compact star-burst. Limitations on size and mass lead us to favor the AGN scenario, but additional studies are required to settle this question. In either case, the wind with its implied mass outflow rate will quench the nuclear power source within the very short time of 5-25 Myr. It is possible, however, that the gas is unable to escape the galaxy and may eventually fall back onto NGC 1377 again.