1. A wireless communication apparatus comprising: a wireless processing unit that performs wireless communication; and an application processing unit that executes an application, wherein the wireless processing unit comprises: an update detecting unit that detects reception of wireless function update information for updating a function of the wireless processing unit when update information for updating any function of the wireless communication apparatus is received; and an update processing unit that updates the function of the wireless processing unit, if the reception of wireless function update information is detected by the update detecting unit, by performing an update process specified in the wireless function update information by a wireless layer-2 protocol without transmitting the wireless function update information to the application processing unit that executes the application stored in the wireless communication apparatus by a processor for the application, wherein the wireless processing unit receives the wireless function update information when the wireless communication apparatus performs a wireless function update process, and receives data other than the wireless function update information when the wireless communication apparatus performs a normal data communication process, the wireless processing unit controls respective protocols defined in a physical layer (PHY), a data link layer, and a network layer from among protocols having the physical layer (PHY), the data link layer, the network layer, a transport layer, and an application layer to perform wireless communication, the update detecting unit of the wireless processing unit acquires an Internet Protocol (IP) packet that has been assembled after controlling the physical layer (PHY) and the data link layer from wireless signals transmitted and received using protocols of upper layers that are equal to or higher than the transport layer and detects the reception of the wireless function update information including a program and/or data that define the update process for updating the function of the wireless processing unit when header information of the Internet Protocol (IP) packet corresponds to a predetermined pattern that has been previously stored, and the update processing unit of the wireless processing unit assembles a plurality of the Internet Protocol (IP) packets of which reception of wireless function update information has been detected by the update detecting unit to generate the wireless function update information and performs the update process based on the generated wireless function update information to update the function of the wireless processing unit.