このあたりを参照したのでメモ → https://stackoverflow.com/questions/30748480/swift-get-devices-ip-address
Swift3向けにアップデートされているんで、そちらを転載しておきます。

手順

Bridging Headerに以下を記述

#include <ifaddrs.h>

functionに以下を追加

// Return IP address of WiFi interface (en0) as a String, or `nil`
func getWiFiAddress() -> String? {
    var address : String?
    
    // Get list of all interfaces on the local machine:
    var ifaddr : UnsafeMutablePointer<ifaddrs>?
    guard getifaddrs(&ifaddr) == 0 else { return nil }
    guard let firstAddr = ifaddr else { return nil }
    
    // For each interface ...
    for ifptr in sequence(first: firstAddr, next: { $0.pointee.ifa_next }) {
        let interface = ifptr.pointee
        
        // Check for IPv4 or IPv6 interface:
        let addrFamily = interface.ifa_addr.pointee.sa_family
        if addrFamily == UInt8(AF_INET) || addrFamily == UInt8(AF_INET6) {
            
            // Check interface name:
            let name = String(cString: interface.ifa_name)
            if  name == "en0" {
                
                // Convert interface address to a human readable string:
                var hostname = [CChar](repeating: 0, count: Int(NI_MAXHOST))
                getnameinfo(interface.ifa_addr, socklen_t(interface.ifa_addr.pointee.sa_len),
                            &hostname, socklen_t(hostname.count),
                            nil, socklen_t(0), NI_NUMERICHOST)
                address = String(cString: hostname)
            }
        }
    }
    freeifaddrs(ifaddr)
    
    return address
}

Usage

if let addr = getWiFiAddress() {
    print(addr)
} else {
    print("No WiFi address")
}