Taht depends o what Hardware the openwrt is running.
For example a little TP-Link WR703n pocket router has a USB port that is usually meant to receive a USB 3G Modem. Running openwrt that USB port can be repurposed to connect and communicate directly with an Arduino.
I don't have any direct experience with that.
The more common way is to connect the router per Ethernet and TCP/IP to an Ethernet Shield/Arduino.