The artificial pancreas is an emerging concept of closed-loop insulin delivery that aims to tightly regulate the blood glucose levels in patients with type 1 diabetes. This paper considers bias injection attacks on the glucose sensor deployed in an artificial pancreas. Modern glucose sensors transmit measurements through wireless communication that are vulnerable to cyber-attacks, which must be timely detected and mitigated. To this end, we propose a model-based anomaly detection scheme using a Kalman filter and a χ2 test. One key challenge is to distinguish cyber-attacks from large unknown disturbances arising from meal intake. This challenge is addressed by an online meal estimator, and a novel time-varying detection threshold. More precisely, we show that the ordinary least squares is the optimal unbiased estimator of the meal size under certain modelling assumptions. Moreover, we derive a novel time-varying threshold for the χ2 detector to avoid false alarms during meal ingestion. The results are validated by means of numerical simulations.