The new arrival will be the first child for the pair, the actor's rep told Us Weekly.
Dinklage and Schmdit, a theatre director, tied the knot in 2005.
The 41-year-old actor currently plays the political manipulator Tyrion in HBO's medieval drama Game of Thrones.
He has also appeared in the feature films The Station Agent, Prince Caspian, Saint John of Las Vegas and Death at a Funeral.
Dinklage will next co-star with Ryan Kwanten in Knights of Badassdom, which is expected to be released later this year.
Game of Thrones has been renewed for a second season by HBO.
> Game of Thrones star 'requested fight scene'
Watch our interview with Game of Thrones star Emilia Clarke below: