Dynamic optical isolation with all-optical switching capability is in great demand in advanced optical communications and all-optical signal processing systems. Most conventional optical isolators rely on Faraday rotation and are realized using micro/nanofabrication techniques, but it is not always straightforward to incorporate magneto-optical crystals into these compact systems. Here, we report the experimental demonstration of a reconfigurable all-optical isolator based on optical excitation of a gigahertz guided acoustic mode in a micrometre-sized photonic crystal fibre core. This device has remarkable advantages over its passive counterparts, including a large dynamic range of isolation, fast switching capability and reversibility, which provide new functionality that is useful in various types of all-optical systems. Devices based on similar physical principles could also be realized in CMOS-compatible silicon on-chip platforms.