The UNESCO Institute for Statistics offers some student mobility statistics by country in their online database (not by degree level, I'm afraid). It's apparently not possible to give a direct link to a particular item from this database, but you can find the figures you're interested in the section
EDUCATION > Other policy relevant indicators > Number and rates of international mobile students (inbound and outbound).
From that, there are several indicators of interest, e.g.
Mobility indicators > Net flow of internationally mobile students or
Inbound students > Inbound internationally mobile students by country of origin, depending on what you're after exactly.
Generally, you'll have to "play" a while with the database interface to get an interesting view of the data. See the "customize > selection" and "customize > layout" options available in the menu on the top of the tables. In particular, you'll often find some interesting additional variables or filters hidden under the "customize > selection" menu. It may take some time to format the data the way you want.
They used to have a simple, nice interactive map of this data on the following page https://uis.unesco.org/en/uis-student-flow, but it doesn't seem to work anymore (the map seems to load forever without displaying anything). I gave the link anyway in case they eventually fix it.
Another option, more restricted in geographical scope, is the Organization for Economic Co-operation and Development (OECD) online database. They offer some data on mobile students by country of destination (but only for OECD countries), degree level, and field. You'll find several variables of interest in the section
Education and Training > Education at a Glance > Students, access to education and participation (e.g. "International graduates by country of origin", "Share of international students and all students by field", etc.) Look also at other variables without "mobile" or "international" in their names, sometime they include filters relative to international students, so it might interest you. Here is an example for doctoral students: https://stats.oecd.org//Index.aspx?QueryId=118857 . Like the UNESCO database, it requires some time to get how the database works, so you'll have to invest some time to find what you're after. Hopefully the links I gave previously will help you.
Otherwise, if you're interested in some particular countries, it may be worth looking at the websites of national statistical institutes or higher education ministers, they often offer data and figures relative to international students.