Arsenene, arsenic analogue of graphene, as an emerging member of two-dimensional semiconductors (2DSCs), is quite promising in next-generation electronic and optoelectronic applications. The metal electrical contacts play a vital role in the charge transport and photoresponse processes of nanoscale 2DSC devices and even can mask the intrinsic properties of 2DSCs. Here, we present a first comprehensive study of the electrical contact properties of monolayer (ML) arsenene with different electrodes by using ab initio electronic calculations and quantum transport simulations. Schottky barrier is always formed with bulk metal contacts owing to the Fermi level pinning (pinning factor S = 0.33), with electron Schottky barrier height (SBH) of 0.12, 0.21, 0.25, 0.35, and 0.50 eV for Sc, Ti, Ag, Cu, and Au contacts and hole SBH of 0.75 and 0.78 eV for Pd and Pt contacts, respectively. However, by contact with 2D graphene, the Fermi level pinning effect can be reduced due to the suppression of metal-induced gap states. Remarkably, a barrier free hole injection is realized in ML arsenene device with graphene-Pt hybrid electrode, suggestive of a high device performance in such a ML arsenene device. Our study provides a theoretical foundation for the selection of favorable electrodes in future ML arsenene devices.