Ron Coderre wrote...
I was on the fence about that formula...negative values cause incorrect
returned values. Hence, the array formula I posted.
....

If there were negative values, MIN would return the negative value
with the greatest absolute value. If negative and positive values are
possible, continuity means zero values should also be excluded.

Most questions like this arise when there are only positive and zero
values. Anyway, if you want to be safe, LARGE is just as [in]efficient
as SMALL, so use either

=LARGE(rng,COUNTIF(rng,"0"))

or the array formula

=MIN(IF(rng0,rng))