Post-quantum cryptography (PQC) is becoming an increasingly important field of study as the advance of quantum computers are expected to one day threaten the public-key cryptographic schemes used today. Although technical standards for PQC are emerging, successful implementation for organisations depends on more than just replacing the cryptographic algorithms. This study aims to find the main organisational barriers that hinder the successful implementation of PQC. This was done by conducting a systematic literature review and analysing the data to create a thematic analysis set on identifying recurring organisational barriers. The results showcase that implementation is primarily hindered by legacy systems and integration challenges, followed by insufficient strategic governance and migration readiness, external dependencies, regulatory and standards uncertainty, lack of expertise and resource constraints. The findings indicate that PQC isn’t only a technical problem but a wider socio-technical problem. The study concludes that organisations require better migration planning, improved internal expertise, clearer regulatory guidance and stronger coordination with external actors for organisations to successfully implement PQC.