"not present or found, absent," 1520s, present-participle adjective from miss (v.). Military sense of "not present after a battle but not known to have been killed or captured" is from 1845. As a noun by 1855.
Missing link was used in various figurative senses before is attested 1846 in reference to forms of plant and animal life [Chambers, "Vestiges of the Natural History of Creation"]; in reference to a hypothetical creature between man and the apes, as a component of Darwin's theory of evolution, by 1860.
But then, where are the missing links in the chain of intellectual and moral being? What has become of the aspirants to the dignity of manhood whose development was unhappily arrested at intermediate points between the man and the monkey? It will not be doubted, we presume, that there exists at present an enormous gap between the intellectual capabilities of the lowest race of men and those of the highest race of apes; and if so, we ask again, why should the creatures intermediate to them--exalted apes or degraded men--have been totally exterminated, while their less worthy ancestors have successfully struggled through the battle of life? [William Hopkins, "Physical Theories of the Phenomena of Life," Fraser's Magazine, July, 1860]
In a popular religious tract of the late 1850s, "The Missing Link of the London Poor," the missing link was the Bible. Missing person, one who has disappeared and whose condition, whether alive or dead, is unknown, is by 1820.