Tobit model censored data arise in multiple engineering applications through saturating sensors, limit-of-detection effects, and image frame effects. In this brief, we introduce a novel formulation of the Kalman filter for Tobit Type 1 censored measurements. Our proposed formulation, called the Tobit Kalman filter, is identical to the standard Kalman filter in the no-censoring case. At or near the censored region, the Tobit Kalman filter utilizes a local approximation of the probability of censoring in order to provide a fully recursive estimate of the state and state error covariance. The additional computational burden of the method compared with the standard Kalman filter is limited to the calculation of m normal probability density functions and m normal cumulative density functions per update, where m is the number of measurements.