I think you already have the "best" solution.
If you want to show off more functional/F#-isms, you could do e.g.
[1..100]
|> Seq.map (function
| x when x%5=0 && x%3=0 -> "FizzBuzz"
| x when x%3=0 -> "Fizz"
| x when x%5=0 -> "Buzz"
| x -> string x)
|> Seq.iter (printfn "%s")
and use lists, sequences, map, iter, patterns, and partial application.
[1..100] // I am the list of numbers 1-100.
// F# has immutable singly-linked lists.
// List literals use square brackets.
|> // I am the pipeline operator.
// "x |> f" is just another way to write "f x".
// It is a common idiom to "pipe" data through
// a bunch of transformative functions.
Seq.map // "Seq" means "sequence", in F# such sequences
// are just another name for IEnumerable<T>.
// "map" is a function in the "Seq" module that
// applies a function to every element of a
// sequence, returning a new sequence of results.
(function // The function keyword is one way to
// write a lambda, it means the same
// thing as "fun z -> match z with".
// "fun" starts a lambda.
// "match expr with" starts a pattern
// match, that then has |cases.
| x when x%5=0 && x%3=0
// I'm a pattern. The pattern is "x", which is
// just an identifier pattern that matches any
// value and binds the name (x) to that value.
// The "when" clause is a guard - the pattern
// will only match if the guard predicate is true.
-> "FizzBuzz"
// After each pattern is "-> expr" which is
// the thing evaluated if the pattern matches.
// If this pattern matches, we return that
// string literal "FizzBuzz".
| x when x%3=0 -> "Fizz"
// Patterns are evaluated in order, just like
// if...elif...elif...else, which is why we did
// the 'divisble-by-both' check first.
| x when x%5=0 -> "Buzz"
| x -> string x)
// "string" is a function that converts its argument
// to a string. F# is statically-typed, so all the
// patterns have to evaluate to the same type, so the
// return value of the map call can be e.g. an
// IEnumerable<string> (aka seq<string>).
|> // Another pipeline; pipe the prior sequence into...
Seq.iter // iter applies a function to every element of a
// sequence, but the function should return "unit"
// (like "void"), and iter itself returns unit.
// Whereas sequences are lazy, "iter" will "force"
// the sequence since it needs to apply the function
// to each element only for its effects.
(printfn "%s")
// F# has type-safe printing; printfn "%s" expr
// requires expr to have type string. Usual kind of
// %d for integers, etc. Here we have partially
// applied printfn, it's a function still expecting
// the string, so this is a one-argument function
// that is appropriate to hand to iter. Hurrah!