I've been trying to figure that out too. From what I can gather, the issue for sailing was not so much with the rain as it was the wind. From April to August, the monsoon winds blew northeast from the sea along Africa up toward India. Since the ships used sail, they could use these winds to sail toward India. From December to March, the prevailing monsoon winds blew southwest, from India toward northeast Africa, and the ships were able to sail back in that direction then. (at least that's what it says in a book I have called Trade and Civilisation in the Indian Ocean, although it only goes to 1750).
Another book I have (The Indian Ocean - catchy title, isn't it?) says that the eastern Arabian Sea off the west coast of India was subject to violent tropical storms in October and November, and that ships usually waited till December to sail west from India. In March the winds would turn and to come out of the southwest and blow toward the northeast, and then in June and July and much of August it again became too stormy to sail. The monsoon also affected the west coast of Maylasia, in the same way as it did the west coast of India. I gather that the seas east of Ceylon (Sri Lanka) tended to be becalmed at this time. Once you get as far south as the Equator, or perhaps 10 degrees south of it, the monsoon is no longer a factor.
I gather, from the weather maps in this book, that the monsoon winds also affected the east coast of India, but even if they did, I don't know whether they would be as strong. The book only mentions sailing between Calicut on the one hand (west coast of India) and Aden and Mogadishu (Arabia and Africa) on the other. So the monsoons would certainly have affected sailing from Bombay and Surat on the west coast. But I don't know how much effect they would have had on shipping from Calcutta or Madras.