Many volcanic systems around the world are located beneath, or in close proximity to, ice caps. Mass change of these ice caps causes surface movements, which are typically neglected when interpreting surface deformation measurements around these volcanoes. These movements can however be significant, and may closely resemble movements due to magma accumulation. Here we show such an example, from Katla volcano, Iceland. Horizontal movements observed by GPS on the flank of Katla have led to the inference of significant inflow of magma into a chamber beneath the caldera, starting in 2000, and continuing over several years. We use satellite radar interferometry and GPS data to show that between 2001 and 2010, the horizontal movements seen on the flank can be explained by the response to the long term shrinking of ice caps, and that erratic movements seen at stations within the caldera are also not likely to signify magma inflow. It is important that interpretations of geodetic measurements at volcanoes in glaciated areas consider the effect of ice mass change, and previous studies should be carefully reevaluated.