I am student traveling to Japan to work on a collaborative project in a Japanese university for less than 60 days. I hold F-1 visa and my country of origin does not have visa free entry to Japan. I am currently in U.S. What type of Visa do I need to obtain?
As an F-1 visa holder, you could apply through the Embassy of Japan in the United States (which does exclude applications from those in B1-B2 status).
If the partner university in Japan does not consider you a researcher and, thereby, requiring a work visa, what you describe appears to fit within Internship (at number 7) for Study, Cultural Activities, and Related Visas:
A short-term work experience in which undergraduate/graduate students receive training and gain experience in a specific field or career area, and which constitutes a part of an academic program
Requirements for Internship varies case-by-case. Please inquire the visa office for the specific requirements before making an application.
Of particular note is that compensation, your stipend, is permissible in this category.
Refer to the Consulate-General of Japan in the United States guide for the office in your region, including web site and email.
In your case, I think the most appropriate visa is actually the "Temporary Visitor" visa. Here are the activities allowed for by this visa (according to the Japanese Consulate-General in Boston):
○ sightseeing; recreation; sports
○ visiting relatives, friends, or acquaintances; visiting a sick person; attending a wedding or funeral ceremony
○ participating in athletic tournaments; contests etc. as an amateur
○ business purposes (such as market research, business liaison, business consultation, signing a contract, or providing after-sale service for imported machinery)
○ inspecting or visiting plants, trade fairs etc.
○ attending lectures, explanatory meetings etc.; academic surveys or research presentations
○ religious pilgrimages or visits
○ friendship visits to sister cities, sister schools etc
○ or other similar activities during a short period of stay in Japan
"Profit-making operations and paid activities" are explicitly excluded.
This page doesn't include short-term research collaborations explicitly, but this is (indeed) an activity rather similar to some of the outlined activities (you can consider it a form of business visit, if you consider academia a form of business).
From personal experience, this is usually allowed. For exactly this purpose (working with a Japanese research collaborator), I have been issued Temporary Visitor Visa without any problems. No questions asked at all; all I need was to show an invitation form and letter signed by my host.
I do not know if your expenses will be covered by the Japanese host institution, but IIRC, if no money is going into your pockets, this should be fine. The aforementioned page even contains a section on the financial documents to provide if "expenses are borne by the Japanese institution".
In any case, please do email the consulate-general or embassy that has jurisdiction in your region. They will advise you on the visa you need, and of course they're much more authoritative than I am.
However, if you will be formally appointed a position as a researcher, it is likely that you will need a visa other than a Temporary Visitor Visa, and that will take much longer. A Temporary Visitor Visa takes only ~3-5 business days to process usually. If you're being paid directly for your work there by the host institution, you'll almost certainly need a work visa.