Monsoon starts in Kerala by June and ends with July. Aug will be a good time for Kerala trip even if you encounter some drizzle don't worry after all it's what make Kerala scenic.
I would request you to visit Kerala during August because it's the after-monsoons that makes the land more green and I'm pretty sure you'll enjoy because Kerala indeed is very beautiful.
Monsoon season between June and August is the best time to visit Kerala for Ayurveda treatments. The wet and cold climate in monsoon weather is ideal and Best time to Visit Kerala