No. Spell-like abilities are not spells.
Does a creature that can use spell-like abilities that simulate arcane spells suffer the -4 to a save vs. a Feeblemind spell?
Spells are NOT spell-like abilities and vice versa. Therefore, creatures do NOT take the -4 penalty due to spell-like abilities. Note, however, that many creatures such as dragons and rakshasa can and do cast spells. They would take the penalty.
Also note that a creature or character effected by this spell can still use its spell-like abilities under most circumstances (as spell-like abilities aren't usually governed by an ability score, though there are exceptions).