If you are willing to accept the expanded Dune universe, it's slightly addressed, but I don't think Frank Herbert ever actually addressed it in the original novels.
In House Corrino by Brian Herbert and Kevin J. Anderson, however, you get the following:
The axis of spin for the planet Arrakis is at right angles to the
radius of its orbit. The world itself is not a globe, but more a
spinning top somewhat fat at the equator and concave toward the poles.
There is a sense that this may be artificial, the product of some
—Report of the Third Imperial Commission on Arrakis
Frank Herbert put a lot of work into studying culture and society, and even quite a bit of biology, but I don't think he thought a lot about orbital mechanics; that said, if you take the expanded works into account (and the above quote), with no axial tilt, you could indeed have day and night, as long as you were even slightly away from the pole. Add in the fact that the map we all know from the book was drawn by a cartographer, but from a map sketched by Herbert (thus making the distances a bit questionable), and it suggests most of the locations in the stories were far enough away from the pole to have more normal day and night.
Per secondhand information, this data is supposed to have been confirmed by Kevin Herbert and Brian Anderson as having come from Frank Herbert's notes.
(Incidentally, this is supported by the contents of the The Dune Encyclopedia which indicates that it has a the axis of rotation almost perpendicular to its ecliptic plane, but it then goes on to mention the impact of other planets in the system giving it an eccentric orbit (and strange, severe season, with a year lasting from 295 to 595 days), and the moons giving it an eccentric rotation and thus a very inconsistent length of day -- averaging 22.4 hours, but ranging from 3.8 to 51.4 hours each. [I don't recall either of these elements in the stories, and they seem like the kind of things that would have come up; honestly -- I'd expect them in Yueh's briefing near the beginning.])
That said, items in The Dune Encyclopedia are contradicted by Heretics of Dune and Chapterhouse Dune, so it may not be the best source. Herbert himself says, in the forward: "As the first 'Dune fan,' I give this encyclopedia my delighted approval, although I hold my own counsel on some of the issues still to be explored as the Chronicles unfold.")
There are some other inconsistencies; for example, in Dune Messiah, in which Scytale is in Arrakeen, we see:
It was the proper hour, though. The pale sun stood almost directly overhead. People of this quarter remained sealed in their houses to sleep through the hot part of the day.
Based on the map, and the position of Arrakeen (on the 60° line), that shouldn't be possible, even allowing for the zero axial tilt; it would still be about 30 degrees off of directly overhead -- well within the range of what he would have noticed. (60° is close to the edge of the arctic circle on earth, by comparison.) It's possible, however, that this is his perception, not reality.
All that said, there are quite a few small inconsistencies in the Dune books (even in the first one, look at Farok and his arm, identified as missing.. but then he clasps his hands together, or things Duncan remembers that would have occurred after he died defending Paul; there are a lot of small issues like these.) I prefer to think of them as historical works that have inaccuracies creep into them over time, much like the quotes or information at the start of the chapters, in effect, coming from a slightly unreliable narrator.