Yes, cyclones (tropical cyclones) frequently form in the Indian Ocean, particularly in two basins:
Warm waters, high humidity, and favorable wind patterns make this the more active basin. Cyclones here often affect India, Bangladesh, Myanmar, and Sri Lanka.
Cyclogenesis also occurs here, though less frequently. Storms can impact the Arabian Peninsula, Pakistan, and western India.
Both basins see peak activity during pre-monsoon (April–June) and post-monsoon (October–December) periods.