Length-$q$ substrings, or $q$-grams, can represent important characteristics of text data, and determining the frequencies of all $q$-grams contained in the data is an important problem with many applications in the field of data mining and machine learning. In this paper, we consider the problem of calculating the {\em non-overlapping frequencies} of all $q$-grams in a text given in compressed form, namely, as a straight line program (SLP). We show that the problem can be solved in $O(q^2n)$ time and $O(qn)$ space where $n$ is the size of the SLP. This generalizes and greatly improves previous work (Inenaga & Bannai, 2009) which solved the problem only for $q=2$ in $O(n^4\log n)$ time and $O(n^3)$ space.