An interesting question. I do not believe that the missions had offical seals. There is no reference to them in the definitive books on the missions written by Fr. Zephrin Egelhardt in 1920s and 1930s. He does discuss a seal for the first bishop of California.
Most cities and major towns have seals. The Seal is an official device of the municipal government, utilized as a mark of authorization and decree. Most seem to have been adopted in 19th century and they typically evolve. Official seals like this often incorporate an image of one of the early / seminal town structures, which often would be a mission. See the attached seal for the city of Santa Clara which calls itself The Mission City and features an image of the mission.
I am curious as to what you are referring to as the "offical seal." If you have a digital copy of one or two (like San Diego or San Francisco) email them to me and we will see if we can research this further.