I've done serious research in Swedish records for almost nine years so I can tell you a bit about what you are facing.
As mentioned in a different answer, Sweden does not have birth, marriage, and death certificates. Instead, they entered that information into the parish registers for births, marriages, and deaths, and into other parish records similar in format to a census but updated continually and not just every ten years. Records were kept in the parish (not nation-wide), so you need to find a clue to the parish where she lived at any point in her life in Sweden. Those Swedish parish records are definitely online (despite what one of your answers says), but they are on fee-based sites. These are scans of the original handwritten parish records and are, of course, in Swedish only (except for some Latin). The first two sites market to people outside of Sweden as well as inside, so there are some pages explaining how to join, etc. which are in English.
http://www.genline.comhttp://www.genline.com (This site has more of the older records. It is starting to post records after 1900 but isn't very complete yet.)
http://www.svar.ra.sehttp://www.svar.ra.se (This site has many fewer of the older records but more of the post-1900 records.)
There is another site which does not yet market to Americans but it has the best images. Its images are far from being complete, however.
However, there are a couple thousand parishes in Sweden, so trying to find "Mary" (who was probably called Maria in Sweden. Maja is also a form of Maria. Mary was probably never used in Sweden back then.) without a parish or a last name or a complete birthdate is probably close to impossible.
Munsson is not a Swedish spelling. It is probably an attempt to spell Månsson = son of Måns (or Månsdotter = daughter of Måns). Måns is a form of Magnus, so she also might have been called Magnusdotter (and brothers might have been called Magnusson) IF that is the name used. Swedes mostly used the patronymic naming customs back then, where the last name of the children was made from the given name of the father plus a possessive s and then "son" for males and "dotter" for females.
This site tells the sort of information usually needed to find our Swedes in Swedish records.
You can obtain a booklet with an overview of Swedish genealogy, plus ideas on how to find clues to the Swedish origins of your ancestor. The following url has a link to downloading the free booklet and also a link to ordering the booklet to be sent by mail. The booklet comes very quickly, so it is better than using up a lot of ink and paper copying the download.
If they still lived in Iowa at the time of the 1925 Iowa State Census, that census provides the names of the parents (including mother's maiden name!!!!) of every enumerated person.
Many of us have been able to find the parish where our Swedes were born by using the resources of the Swenson Swedish Immigration Research Center. The Swenson Center has a website but their extensive collection of records is NOT online. We need to go there to research or pay them to research for us. They have records which are difficult or even impossible to find elsewhere.
Post on the Sweden board for further help once you have more information about "Mary". Type Sweden into the "Post to Forum" board on the top right of this page.
I do see this person emigrating with the same month andyear of birth and year of emigration mentioned in a different message,but unless you can find better information, I have no idea if she is yours. This comes from a Swedish cd called Emibas, made from registrations in the Swedish parish to go to a foreign country. It is about 75% complete. (As I said earlier, Magnusdotter is the same name as Månsdotter and Munson/Munsdotter are absolutely not spellings used in Sweden. It is an Americanization of Månsson.)
Magnusdotter, Maria Kristina Piga = maid. (unmarried woman)
b. 3/30/1868 in Grava, Värmlands län (Värmland)
Emigrated 4/29/1893 from Sundsvall, Sundsvall, Västernorrlands län (Medelpad) to Nordamerika