Sex determination systems in plants can involve either female or male heterogamety (ZW or XY, respectively). Here we used Illumina short reads, Oxford Nanopore Technologies (ONT) long reads and Hi-C reads to assemble the first chromosome-scale genome of a female willow tree (Salix dunnii), and to predict genes using transcriptome sequences and available databases. The final genome sequence of 328 Mb in total was assembled in 29 scaffolds, and includes 31,501 predicted genes. Analyses of short-read sequence data that included female and male plants suggested a male heterogametic sex-determining factor on chromosome 7, implying that, unlike the female heterogamety of most species in the genus Salix, male heterogamety evolved in the subgenus Salix. The S. dunnii sex-linked region occupies about 3.21 Mb of chromosome 7 in females (representing its position in the X chromosome), probably within a pericentromeric region. Our data suggest that this region is enriched for transposable element insertions, and about one-third of its 124 protein-coding genes were gained via duplications from other genome regions. We detect purifying selection on the genes that were ancestrally present in the region, though some have been lost. Transcriptome data from female and male individuals show more male- than female-biased genes in catkin and leaf tissues, and indicate enrichment for male-biased genes in the pseudo-autosomal regions. Our study provides valuable genomic resources for further studies of sex-determining regions in the family Salicaceae, and sex chromosome evolution.