Lwt [1] based web frameworks can be used on MirageOS if they provide an interface that allows someone to swap out the unix dependent pieces. One such framework is Opium [2], that provides most of its features in a unix independent code library `opium_kernel`. Its fairly straightforward to run an opium app on mirage. This example needs to be updated to the newest apis in the released version of Opium but this can provide some hints about how to run an opium app on mirage: https://github.com/anuragsoni/ocaml-opium-unikernel.
If a lower level web toolkit is sufficient then ocaml's cohttp [3] library has been available on mirage for quite some time now.
[1] https://github.com/ocsigen/lwt/