I haven't had time to read the comments so perhaps someone has already answered the question. Both of my mother's parents were from Sweden. My grandfather became a US citizen, my grandmother did not automatically become naturalized through him, in fact never did become a citizen. My mother was born in 1921 so we're talking about the same period of time.
The status of a married immigrant seems to have varied considerably. There is a good article here:
http://www.archives.gov/publications/prologue/1998/summer/women-and-naturalization-1.html
“There were certain legal and social provisions, however, governing which women did and did not go to court to naturalize. In general, immigrant women have always had the right to become U.S. citizens, but not every court honored that right. Since the mid-nineteenth century a succession of laws worked to keep certain women out of naturalization records, either by granting them derivative citizenship or barring their naturalization altogether. It is this variety of laws covering the history of women’s naturalization, as well as different courts’ varying interpretation of those laws, that help explain whether a naturalization record exists for any given immigrant woman.”
However, in this decision, the court never refers to her father’s status in any discussion of citizenship. It seems to consider that irrelevant as well, and to take her birth in NY as evidence that she was a citizen, a native citizen, and a natural born citizen.
Hmm. What year was your grandfather naturalized and what year were they married. All women who were married to naturalized US Citizens became US citizens ipso facto until the law was changed in 1922. By the way, out of curiosity, how do you know that your grandmother was not a citizen? If your grandparents were married in 1920 and in the US then maybe the 1920 US census would tell you if you haven't already seen it.