Yes. Next.js can run on a virtual private server as a Node.js server, in a Docker container, or as a static export. The right mode depends on which Next.js features the application uses.
Pick the deployment mode first
A standard Node.js deployment runs next build and next start and supports all Next.js features. Standalone output packages a smaller traced runtime. Docker can package the same full-featured server. A static export can be served by Nginx alone, but features that require a server are unavailable.
Treat the VPS as infrastructure
The server needs a supported runtime, enough memory for the build or a separately built artifact, disk for releases and caches, and network access to application dependencies. Put a reverse proxy in front of the Next.js process, terminate TLS, and supervise the process so it starts after reboot and restarts after failure.
A single persistent server naturally keeps its local Next.js cache on disk. Multiple instances require deliberate shared-cache and invalidation design to avoid inconsistent results.
Size from evidence
Build the production application and test representative routes under load. Observe peak memory, CPU saturation, response latency, image work, and data-source limits. Leave headroom for deploys and traffic bursts, or build artifacts elsewhere so compilation cannot starve the live process.
The key tradeoff is simple: a VPS gives you broad control and often predictable resources, while making your team responsible for keeping the full service healthy.