The International Classification of Diseases (ICD) is a system for systematically recording patients' diagnoses. Clinicians or professional coders assign ICD codes to patients' medical records to facilitate funding, research, and administration. In most health facilities, clinical coding is a manual, time-demanding task that is prone to errors. A tool that automatically assigns ICD codes to free-text clinical notes could save time and reduce erroneous coding. While many previous studies have focused on ICD coding, research on Swedish patient records is scarce. This study explored different approaches to pairing Swedish clinical notes with ICD codes. KB-BERT, a BERT model pre-trained on Swedish text, was compared to the traditional supervised learning models Support Vector Machines, Decision Trees, and K-nearest Neighbours used as the baseline. When considering ICD codes grouped into ten blocks, the KB-BERT was superior to the baseline models, obtaining an F1-micro of 0.80 and an F1-macro of 0.58. When considering the 263 full ICD codes, the KB-BERT was outperformed by all baseline models at an F1-micro and F1-macro of zero. Wilcoxon signed-rank tests showed that the performance differences between the KB-BERT and the baseline models were statistically significant.