The impact of reactive school closure on an epidemic is uncertain, since it is not clear how an unplanned closure will affect social mixing patterns. The effect of school holidays on social mixing patterns is better understood. Here, we use mathematical models to explore the influence of the timing of school holidays on the final size and peak incidence of an influenza-like epidemic. A well-timed holiday can reduce the impact of an epidemic, in particular substantially reducing an epidemic's peak. Final size and peak incidence cannot both be minimized: a later holiday is optimal for minimizing the final size, while an earlier holiday minimizes peak incidence. Using social mixing data from the UK, we estimated that, had the 2009 influenza epidemic not been interrupted by the school summer holidays, the final size would have been about 20% larger and the peak about 170% higher.