Grace, 39, and Hinshaw, 28, got engaged in January 2015 and married last May.
People magazine reported that Grace and Hinshaw were spotted walking to the Sweet Butter Kitchen in Los Angeles on Saturday, when paparazzi noticed Hinshaw's baby bump.
The child is the first for Hinshaw and Grace, but Grace is godfather to actress Jaime King's son, James. Jessica Alba is James' godmother.
Grace is not the only "That '70s Show" star to be expecting a child this year. Grace's former co-star and former TV girlfriend, Laura Prepon, is also expecting a baby girl with her fiancé, Ben Foster, later this summer.