In the fission yeast S. pombe, nuclei are actively positioned at the cell center by microtubules. Here, we show that cytoplasmic microtubules are mechanically coupled to the nuclear heterochromatin through proteins embedded in the nuclear envelope. This includes an integral outer nuclear membrane protein of the KASH family (Kms2) and two integral inner nuclear membrane proteins, the SUN-domain protein Sad1 and the previously uncharacterized protein Ima1. Ima1 specifically binds to heterochromatic regions and promotes the tethering of centromeric DNA to the SUN-KASH complex. In the absence of Ima1, or in cells harboring mutations in the centromeric Ndc80 complex, inefficient coupling of centromeric heterochromatin to Sad1 leads to striking defects in the ability of the nucleus to tolerate microtubule-dependent forces, leading to changes in nuclear shape, loss of spindle pole body components from the nuclear envelope, and partial dissociation of SUN-KASH complexes. This work highlights a framework for communication between cytoplasmic microtubules and chromatin.