In the framework of error correction in space telecommand (TC) links, the Consultative Committee for Space Data Systems (CCSDS) currently recommends short block-length BCH and binary low-density parity-check (LDPC) codes. Other alternatives have been discarded due to their high decoding complexity, such as non-binary LDPC (NB-LDPC) codes. NB-LDPC codes perform better than their binary counterparts over AWGN and jamming channels, being great candidates for space communications. We show the feasibility of NB-LDPC coding for space TC applications by proposing a highly efficient decoding architecture. The proposed decoder is implemented for a (128,64) NB-LDPC code over GF(16) and the design is particularized for a space-certified Virtex-5QV FPGA. The results prove that NB-LDPC coding is an alternative that outperforms the standardized binary LDPC, with a coding gain of 0.7 dB at a reasonable implementation cost. Given that the maximum rate for TC recommended by the CCSDS is 2 Mbps, the proposed architecture achieves a throughput of 2.03 Mbps using only 9615 LUTs and 5637 FFs (no dedicated memories are used). In addition, this architecture is suitable for any regular (2,4) NB-LDPC (128,64) code over GF(16) independently of the H matrix, allowing flexibility in the choice of the code. This brief places NB-LDPC codes as the excellent candidates for future versions of the telecommand uplink standard. This work was supported by Spanish MICINN/AEI under Project TEC2017-86722-C4-3-R.