TV Tropes has quite a collection of Myer's Briggs descriptions for fictional characters and their lists match quite a few I have seen over the years.
Hermione Granger is listed there as an ISTJ. Introverted, Sensing, Thinking, Judging. ISTJs are orderly, dependable, practical and dutiful above all. They prefer working with facts and can be conservative in their loyalty to traditions.
From the Personality Profiler:
As an ISTJ, your primary mode of living is focused internally, where you take things in via your five senses in a literal, concrete fashion. Your secondary mode is external, where you deal with things rationally and logically.
ISTJs are quiet and reserved individuals who are interested in
security and peaceful living. They have a strongly-felt internal sense
of duty, which lends them a serious air and the motivation to follow
through on tasks. Organized and methodical in their approach, they can
generally succeed at any task which they undertake.
ISTJs are very loyal, faithful, and dependable. They place great
importance on honesty and integrity. They are "good citizens" who can
be depended on to do the right thing for their families and
communities. While they generally take things very seriously, they
also usually have an offbeat sense of humor and can be a lot of fun -
especially at family or work-related gatherings.
ISTJs tend to believe in laws and traditions, and expect the same from
others. They're not comfortable with breaking laws or going against
the rules. If they are able to see a good reason for stepping outside
of the established mode of doing things, the ISTJ will support that
effort. However, ISTJs more often tend to believe that things should
be done according to procedures and plans. If an ISTJ has not
developed their Intuitive side sufficiently, they may become overly
obsessed with structure, and insist on doing everything "by the book".
The ISTJ is extremely dependable on following through with things
which he or she has promised. For this reason, they sometimes get more
and more work piled on them. Because the ISTJ has such a strong sense
of duty, they may have a difficult time saying "no" when they are
given more work than they can reasonably handle. For this reason, the
ISTJ often works long hours, and may be unwittingly taken advantage
of.
The ISTJ will work for long periods of time and put tremendous amounts
of energy into doing any task which they see as important to
fulfilling a goal. However, they will resist putting energy into
things which don't make sense to them, or for which they can't see a
practical application. They prefer to work alone, but work well in
teams when the situation demands it. They like to be accountable for
their actions, and enjoy being in positions of authority. The ISTJ has
little use for theory or abstract thinking, unless the practical
application is clear.
ISTJs have tremendous respect for facts. They hold a tremendous store
of facts within themselves, which they have gathered through their
Sensing preference. They may have difficulty understanding a theory or
idea which is different from their own perspective. However, if they
are shown the importance or relevance of the idea to someone who they
respect or care about, the idea becomes a fact, which the ISTJ will
internalize and support. Once the ISTJ supports a cause or idea, he or
she will stop at no lengths to ensure that they are doing their duty
of giving support where support is needed.
The ISTJ is not naturally in tune with their own feelings and the
feelings of others. They may have difficulty picking up on emotional
needs immediately, as they are presented. Being perfectionists
themselves, they have a tendency to take other people's efforts for
granted, like they take their own efforts for granted. They need to
remember to pat people on the back once in a while.
ISTJs are likely to be uncomfortable expressing affection and emotion
to others. However, their strong sense of duty and the ability to see
what needs to be done in any situation usually allows them to overcome
their natural reservations, and they are usually quite supporting and
caring individuals with the people that they love. Once the ISTJ
realizes the emotional needs of those who are close to them, they put
forth effort to meet those needs.
- Dedicated, forthright, strong sense of internal purpose and duty describe Hermione perfectly.
- Hermione is eminently logical and the brains of Team Potter. They rely on her to remember the important things and she is often overlooked when Team Potter's contributions are considered.
- Hermione has show she is dedicated to the magical traditions, makes
amazing efforts to master her craft, so much so, she would use
temporal magicks to get more time to study and learn.
- Her perfectionist nature is shown by her absolute necessity to have a
spell for every occasion. Her loyalty to her friends is
unquestionable and unflagging.
- Her emotional reservation displayed with her inability to summon the
Patronus effectively.
This would be an accurate description of Ms. Granger behaviors. While this is not canon, I can certainly see how Hermione Granger fits this Myer's Briggs profile and while we cannot know what J.K. Rowlings might think of the classification, it certainly describes the character Hermione Granger quite well.