It's possible, you just need to configure your webserver to handle it the way you'd expect.
I'd however personally recommend that you set it up on a sub-domain instead of a sub-directory, since it can cause confusion that a route is actually an entirely different application.
Consider placing your API on api.domain.com and the actual app on domain.com.
Have a look at the Deployment section of the Laravel docs for an example NGINX configuration, you would essentially just swap the domain with api.domain.com and point the root accordingly.