If the numbers are *always* positive..
Array entered**:
..=MIN(IF(A1:A10>0,A1:A10))
Or, normally entered:
=SMALL(A1:A10,COUNTIF(A1:A10,0)+1)
If there might be negative numbers...
Array entered**:
=MIN(IF(A1:A10<>0,A1:A10))
** array formulas need to be entered using the key combination of
CTRL,SHIFT,ENTER (not just ENTER). Hold down both the CTRL key and the SHIFT
key then hit ENTER.