This paper presents, optimizes, and analyzes the performance of a novel hybrid Selective Repeat/Multi Copy (SR/MC) Automatic Repeat Request (ARQ) scheme for transmitting fragmented Internet Protocol (IP) packets. The ARQ scheme works in the SR mode until the last IP packet fragment is transmitted. If a fragment is negatively acknowledged after the last fragment is transmitted, then the system goes into the MC mode. In the MC mode, multiple copies of the erroneous fragment are transmitted. After the IP fragments are received without error, the system returns to the SR mode. The optimization of the ARQ is done in terms of two parameters: fragment size and the optimum number of packets to be transmitted in the MC mode, M. Optimum values for both parameters are calculated for Bit Error Rate (BER), throughput, IP packet size, and delay. The fragment size is also calculated for actual data throughput for a given IP packet size, both with and without Forward Error Correction (FEC). Then, the performance of the proposed scheme is evaluated in terms of BER and IP packet size with the optimum M and fragment size. Performance results are obtained with and without Bose Chaudhuri Hocquenghem (BCH) error correction codes under Additive White Gaussian Noise (AWGN) as well as Flat Rayleigh Fading channels. The ARQ scheme gives optimum performance for M equal to 10 fragments and fragment size of 75 bytes. Under the AWGN channel, a throughput of 0.9 is achieved for any IP packet size and at higher BER conditions compared to the Selective Repeat + Stutter Scheme 2 (SR + ST 2). An 8 dB improvement is achieved under the flat Rayleigh fading channel using BCH(63, 51, 2) for a throughput of 0.9.