A warp knit self-curling fabric and methods of construction thereof provides an elongate sleeve having overlapping edges for protecting elongate members. The fabric includes warp stitches and a plurality of weft stitches. The fabric comprises at least three yarns warp knit together, wherein one of the weft stitches is knit using a tricot stitch of a monofilament under tension to bias the fabric into a self-curled configuration about a central space. The monofilament forms an inner surface of the sleeve.