Mineral wool pipe insulation, the mineral wool thereof includes a mix of mineral wool fibers and at least a curable binder being cured. The pipe insulation includes at least two separate elongated partial sections of mineral wool that are inter-connectable to each other around a pipe or container to form an insulation layer encompassing the pipe or container. Each separate partial section being inter-connectable by being provided with interconnecting means along at least two thickness-wise edges thereof. A method of manufacturing mineral wool pipe insulation includes forming each separate partial section of mineral wool by sawing or cutting from a cured block of mineral wool, or by curing a mixture of loose mineral wool fibers and a curable binder in a mold.