I guess it would be something like hypothesis continui. Alternatively, it could also be rendered as hypothesis de continuo.
Note that noun-noun compounds like "continuum hypothesis" or "string theory" are possible in some languages (e.g., English, Mandarin Chinese, A(merican) S(ign) L(anguage), Japanese, etc). In contrast, Latin is not to be classified into the same typological set of languages with regard to the so-called "Compounding Parameter". Typically, these noun-noun compounds are to be rendered into Latin (and Romance languages) differently. In Latin the typical translation involves putting the first member of the English compound in Genitive case: e.g., cf. Engl. string theory = Lat. theoria chordarum. Same with Engl. continuum hypothesis = Lat. hypothesis continui. Alternatively, as pointed out above, the first noun of the English compound can also be rendered in Latin as involving the preposition de plus the substantivized adjective in Ablative case: i.e., hypothesis de continuo. As noted below by Denis Nardin, the latter evolved into the structure found in Romance: e.g., cf. It. ipotesi del continuo.