Traditionally, the welfare assessment of farm animals has focused on health and production outcomes. Positive welfare is, however, not merely the absence of negative welfare and is an important part of a life worth living. Play behaviour is widely considered to be an indicator of positive emotions because it is a “luxury” behaviour. Direct visual observation is considered the most accurate method of behavioural analysis, but it is time consuming and laborious. There is increasing interest in the use of remote monitoring technology to quantify behaviour. We compared the data output (“motion index” (MI)) from a commercially available tri-axial accelerometer fitted to newborn dairy calves to video footage of the same calves, with a focus on play behaviour. The motion index values over 48 h were positively correlated with both the duration of play behaviour and the number of play bouts. The motion index threshold in each sample interval with the optimal sensitivity and specificity for the identification of play behaviour was MI ≥ 2.5 at a 1 min resolution (sensitivity (Se) = 98.0%; specificity (Sp) = 92.9%) and MI ≥ 24.5 at a 15 min resolution (Se = 98.0%; Sp = 89.9%), but these values consistently overestimated the overall proportion of sample intervals in which play was observed. The MI that best reflected the results obtained from visual one-zero sampling was MI ≥ 23 for 1 min intervals and MI ≥ 62 for 15 min intervals—this may therefore be the basis of a more conservative approach to the identification of play behaviour from accelerometer-generated data. Our results indicate that accelerometer-generated data can usefully indicate the amount of play behaviour shown by newborn calves for up to 48 h, providing an efficient method for identifying this important parameter in future work.