There is no hard limit, but it is indirectly constrained by the index size.
That being said, there are numerous indirect limits that affect the facet values at query time:
maxFacetValueslimiting the amount of values sent back with a query (hard limit at 1000)
maxFacetHitslimit the amount of facet values that can be retrieved using
searchForFacetValues(hard limit at 100)
Facet values are not guaranteed to be exhaustive in the result list, but this usually has more impact on counts of each facet value than their actual presence. This is more influenced by the amount of records than the amount of facets.
Also, the amount of facet values for a single record’s attribute are constrained by the record’s size.