Strictly speaking, there are two kinds of abbreviations: the sort where the ends of the words are cut off (e.g. for exempli gratia, etc. for et cetera), and the sort where the middles are dropped out (Mr for Mister, Gk for Greek). In the former, the abbreviation is marked with a period (full-stop) to show that something is missing from the end, but in the latter, a period is not used (though some people put one anyway). To be completely self-consistent, a period in the middle might be called for (“M.r”), but that marks the border between rationality and eccentricity.
So what are we to make of Mrs? The dictionary says that it is an abbreviation (the middle-dropping kind) of Mistress, just like Mr is an abbreviation of Mister. But we don’t actually say “Mistress So-and-so”; instead we say something more like “Missus So-and-so.” The word “mistress” itself has also gone off on its own way, and now refers not to the Missus but to the other Miss that the Mister misses.
To meet the need for a term of address that does not make reference to a woman’s marital status, the neologism Ms was coined, pronounced “Miz”. It looks like an abbreviation, especially when a period is used, but there’s nothing behind the curtain, just like the S. in Harry S. Truman.
These cases say for language what the panda’s thumb says for biology: that evolution makes do with what is available, which often ends up giving us such little puzzles. Writing is more conservative than speech, and it dictates that we should continue to write Mr and Mrs even though we say Mistuh and Missus. The coiners of Ms were fighting against social convention of their time, which defined women in terms of their relationships to men (their fathers or their husbands). They were successful enough in their struggle that we now address women as Ms without a second thought, but the force of written convention is so strong that we still perpetuate the fiction of writing it as if it were an abbreviation.