It clearly would be discriminatory (in the broadest sense) because it creates a distinctive criterion that a priori defines who can, and who cannot, apply. However, ‘discrimination’ is just a synonym that has taken on all the negative connotations of distinguishing (a word with whom it shares a common root) and therefore one should sometimes wonder whether or not all ‘discriminatory’ acts are prima facie ill-advised. If you can rephrase the criterion in terms of distinguishing between different groups you’re (probably) on an ethically defensible high-ground.

Have you asked for a reason for this limitation? For instance, it could be something as simple as undergrad programs providing academic credit for internships, but masters programs not: which affects the employer’s obligation to pay the intern.

In theory, anybody can be an undergrad

In theory, anyone can be named "Chen", "Nguyen", or "Mwangi" but try instituting a policy banning those people from an internship program.