Mutual comprehensibility is a continuum, it is not all or nothing. Americans and English people understand each other, especially if both make an effort to avoid excessively local pronunciations and words. Literate speakers of any of the Scandinavian languages can read most texts in any other Scandinavian language. Most educated Romanians can grasp the meaning of Italian Wikipedia articles without any special training; Spanish Wikipedia articles are less transparent for us, and reading French Wikipedia is not possible at all without actually learning French. Russians are said to be able to follow the main points of an Ukrainian text, and so on.
If the two populations are highly literate, have schools and a common body of literature (fiction, poetry, law, technical all count) then a few centuries won't break their mutual comprehensibility. Americans are a good example – they fled England and for two centuries or so they had limited contact with the mother country, yet their language is still recognizable as a form of English.
On the other hand, if one or both of them descend into illiteracy, then language evolution will be much faster, and three or four centuries may be enough to break the mutual comprehensibility; six or more centuries will almost certainly be enough. For example, the speakers of the earliest forms of French lost mutual comprehensibility with the ancestors of the earliest forms of Italian (and with the Latin books) in about 400 or 500 years (between the 5th and the 9th century). Note that the relationship between the two languages will most likely remain obvious even to ordinary people, but learning to read or speak the other language won't be trivial and will require a certain (probably small) amount of effort.
For linguistic divergence to reach a point where learning the other language is difficult you need more than a few centuries. Even today, after about 15 centuries of separate evolution, speakers of one Romance language find it relatively easy to learn another, and translation between Romance languages is smooth and effortless; and the same can be said about Slavic languages, which have about 12 centuries of separate evolution.