Context. High-resolution millimeter wave very-long-baseline interferometry (mm-VLBI) is an ideal tool for probing the structure at the base of extragalactic jets in detail. The TeV blazar Mrk 501 is one of the best targets among BL Lac objects for studying the nature of off-axis jet structures because it shows different jet position angles at different scales. Aims. The aim of this study is to investigate the properties of the off-axis jet structure through high-resolution mm-VLBI images at the jet base and physical parameters such as kinematics, flux densities, and spectral indices. Methods. We performed Very Long Baseline Array (VLBA) observations over six epochs from 2012 February to 2013 February at 43 GHz. Quasi-simultaneous Global Millimeter VLBI Array (GMVA) observations at 86 GHz were performed in May 2012. Results. We discover a new jet component at the northeast direction from the core in all the images at 43 and 86 GHz. The new component shows the off-axis location from the persistent jet extending to the southeast. The 43 GHz images reveal that the scattering of the positions of the NE component is within ~0.2 mas. The 86 GHz data reveals a jet component located 0.75 mas southeast of the radio core. We also discuss the spectral indices between 43 and 86 GHz, where the northeast component has steeper spectral index and the southeast component has comparable or flatter index than the radio core does.