Intense, short-lived random fears seem to be a pretty normal thing among toddlers. My son is almost 3, and already developed and then mostly overcome fears of bathing, thunder, the vacuum cleaner, bugs, and dog paws (the paws specifically, not even dogs in general!) Some of these are obviously related to loud noises, which is one of the most common toddler fears, the others seem rather unrelated to anything; for example he enjoyed bathing before and after his unexplained and temporary but obviously real fear.
I have so far helped him through this with a combination of reassurance, gentle exposure and explanation. Keep explanations simple, truthful and non-threatening.
With my son, I use words that acknowledge that the fear he feels is real, but confirms his safety. "I see that you feel scared. Mommy and daddy keep you safe." Or "Bugs look scary sometimes, but they don't hurt us."
I use very, very gentle exposure and explanations-- first some age-appropriate books about really 'non scary' bugs like the The Very Hungry Catepillar-- A friendly, not realistic, not creepy bug story. Then after a few days we looked at a more 'scientific' kids books with real photos of various animals, including bugs, being pretty matter of fact about the insect pages (don't 'warn' about the bug pictures or make too big a deal about them). Then when I spotted a ladybug or an ant outdoors I would point it out to let him look, and talk about it, like "Oh a tiny little ladybug! Look how bright red it is! These bugs don't hurt us, but they help the garden grow." I let it walk on me and talked about how it tickled a little and how they walk on 6 feet.
Waiting a while for the stage to pass, without either invalidating his feelings by saying things like "don't be scared" or confirming his belief that he should be scared by taking over the top bug-avoidance measures is another possibility.
If his fear continues to be crippling as far as his day to day activities, doesn't seem to respond to reassurance, seems to be getting worse not better with time, or you are very concerned about his anxiety level in general, it wouldn't hurt to ask his doctor, or see a child therapist for an assessment.
Here's some more info about fears and anxiety in young children: