We present the results of a VLB1 Space Observatory Programme (VSOP) observation of the subparsec structure in Cen A at 4.9 GHz. The observation produced an image of the subparsecjet components with a resolution of three-times better than images from previous VLB1 monitoring campaigns at 8.4 GHz, and twice better than the previous 22 GHz studies. Owing to its proximity, our Cen A space-VLBI image is one of the highest spatial-resolution images of an AGN ever made - 0.01 pc per beam - comparable only to the recent 43 GHz VLBI images of M 87. The elongated core region is resolved into several components of over 10 milliarcsec long (0.2 pc), including a compact component of brightness temperature 2.2x 10(10)K. A counterjet was detected: if we assume jet-counterjet symmetry, a relatively slow jet speed, and a large viewing angle, as derived from previous observations. the image allows us to investigate the distribution of ionized gas around the core, which is opaque at this frequency due to free-free absorption. We also anal zed the jet geometry in terms of collimation. Assuming the strongest component to be the core, the jet opening angle at similar to 5000rs from the core is estimated to be similar to 12 degrees, with the collimation of the jet to similar to 3 degrees continuing out to similar to 20000r(S). This result is consistent with previous studies of the jet in M 87, which favor MHD disk outflow models. Future space VLB1 observations at higher frequencies will probably be able to image C, the collimation region, within 1000r(S) of the center of Cen A, together with the accretion disk itself.