In a packet processing apparatus and method in an ethernet switching system, an introduced packet is discarded by switching to a dummy port instead of trapping the packet until a layer 3 table of an ethernet switch chip is updated, thereby operating an Address Resolution Protocol (ARP) after having minimized a central processing unit (CPU) load. The packet processing apparatus, upon receipt of a first packet headed for a destination Internet protocol (IP) address not existing in the packet processing unit from a source host, transmits an ARP request packet to the destination IP address so as to acquire routing information of a destination host. When the packet processing apparatus receives a second packet headed for the IP address of the destination host from the source host before an ARP response packet is received in accordance with the ARP request packet and before the routing information corresponding to the IP address of the destination host is acquired, it switches the packet based on imaginary routing information.