The first sister missionaries were called in 1898, 68 years after the first male missionary, Samuel Smith. Of course women often played active roles in spreading the gospel informally and several women were called to teach or accompany their husbands on missions, though none were called in a strictly proselyting capacity and none were listed in the official missionary records of the Church. The two women called to be the first sister missionaries were directly tied to Brigham Young Academy.
Lucy Jane (nicknamed “Jennie”) Brimhall Knight was engaged to a full-time missionary but wanted to stay busy. While teaching at Brigham Young Academy in 1896, she dreamed of experiencing the world before becoming a wife and mother. So she set her mind to traveling around Europe with Amanda Inez Knight, her friend and future sister-in-law.
As they excitedly planned out their vacation adventures Jennie’s bishop, J. B. Keeler, encouraged the women to use their expenses to serve the Lord. He suggested serving a mission in Europe. Single sisters were not called to serve missions during this time, so the women, taken a back, said that if they were formally called by the Church president they would go. Bishop Keeler wrote to President Wilford Woodruff about the idea, and he decided to call Jennie and Inez to “serve in Great Britain as the first single LDS sisters to be proselyting missionaries.”
Jennie and Inez served as full-time missionaries in Chiltenham, Oldham, and Bristol, doing “all things required of male missionaries.”
Referring to Jennie and Inez, Orson F. Whitney explained, “The novel spectacle of two young and innocent girls–whose appearance alone betokened modesty and virtue, as their utterances shared intelligence and sincerity–declaring in words of soberness that Mormonism was divine was sufficient to extend the call to other single sisters to share the gospel of Jesus Christ.” 
Jennie’s and Inez’s faith, vigor, and spirit made them special servants of the Lord. Thanks to Jennie and Inez, many sister missionaries have enjoyed the privilege of serving all around the world.
Extension of first sister missionaries: http://www.lds.org/ensign/1980/07/the-first-sister-missionaries
Instant online access to Amanda Inez Knight’s missionary journal: http://contentdm.lib.byu.edu/cdm/search/collection/MMD/mode/all/field/creato/searchterm/allen%20inez
1. The Church of Jesus Christ of Latter-day Saints, “First Latter-day Saint Missionary Born 200 Years Ago Today,” Newsroom, March 2008, http://www.mormonnewsroom.org/article/first-latter-day-saint-missionary-born-200-years-ago-today.
2. Diane Mangum, “The First Sister Missionaries,” LDS.org, July 1980, http://www.lds.org/ensign/1980/07/the-first-sister-missionaries.
3. Jeffrey Hardy, “Amanda Inez Knight,” BYU Harold B. Lee Library, http://webcache.googleusercontent.com/search?q=cache:gtXd5Npko2gJ:lib.byu.edu/digital/mmd/diarists/Allen_Inez.php+&cd=1&hl=en&ct=clnk&gl=us&client=firefox-a.
4. Susan E. Black and Mary J. Woodger, Women of Character: Profiles of 100 Prominent LDS Women, (American Fork, UT, Covenant Communications Inc., 2011), 185-186.