Centrosomes are cellular structures that nucleate microtubules. At their core is a pair of centrioles that recruit pericentriolar material (PCM). Although centrosomes are considered membraneless organelles, in many cell types, including human cells, centrosomes are surrounded by endoplasmic reticulum (ER)-derived membranes of unknown structure and function. Using volume electron microscopy (vEM), we show that centrosomes in the Caenorhabditis elegans (C. elegans) early embryo are surrounded by a three-dimensional (3D), ER-derived membrane reticulum that we call the centriculum, for centrosome-associated membrane reticulum. The centriculum is adjacent to the nuclear envelope in interphase and early mitosis and fuses with the fenestrated nuclear membrane at metaphase. Centriculum formation is dependent on the presence of an underlying centrosome and on microtubules. Conversely, increasing centriculum size by genetic means led to the expansion of the PCM, increased microtubule nucleation capacity, and altered spindle width. The effect of the centriculum on centrosome function suggests that in the C. elegans early embryo, the centrosome is not membraneless. Rather, it is encased in a membrane meshwork that affects its properties. We provide evidence that the centriculum serves as a microtubule "filter," preventing the elongation of a subset of microtubules past the centriculum. Finally, we propose that the fusion between the centriculum and the nuclear membrane contributes to nuclear envelope breakdown by coupling spindle elongation to nuclear membrane fenestration.