What is the best way to break up a shapefile into discretely sized tiles?

TL;DR version: I need to break up road vectors in QGIS to 4,033km2 tiles to import into an UnrealEngine landscape.

I am evaluating a plugin the imports GIS data into UnrealEngine for a simulation. One of the best things about this plugin is that it can import shapefiles to create landscape splines (that’s roads and rivers and such for all the non-game programmer types, since this S.E. is about GIS, not UE). It’s really great, but for landscapes greater than 16km2 or so in UE, you need to import the data into landscape tiles.

I’m using QGIS to grab the overall data area I want, but I need it broken up into tiles. The topography DEM information was easy enough to split into tiles, but I am having a hard time breaking up the shapefile data. Does anyone here know of any tools for taking a larger-area shapefile and breaking it up into chunks of a specific size?