The 1965 North Indian Ocean cyclone season had no bounds, but cyclones tend to form between April and December, with peaks in May and November. The season has no official bounds but cyclones tend to form between April and December. These dates conventionally delimit the period of each year when most tropical cyclones form in the northern Indian Ocean. There are two main seas in the North Indian Ocean—the Bay of Bengal to the east of the Indian subcontinent and the Arabian Sea to the west of India. The official Regional Specialized Meteorological Centre in this basin is the India Meteorological Department (IMD), while the Joint Typhoon Warning Center releases unofficial advisories. An average of four to six storms form in the North Indian Ocean every season with peaks in May and November. Cyclones occurring between the meridians 45°E and 100°E are included in the season by the IMD.

The 1965 Atlantic hurricane season was the first to use the modern-day bounds for an Atlantic hurricane season, which are June 1 to November 30. These dates conventionally delimit the period of each year when most tropical cyclones form in the Atlantic basin. It was a slightly below average season, with 10 tropical cyclones developing and reaching tropical storm intensity. Four of the storms strengthened into hurricanes. One system reached major hurricane intensity – Category 3 or higher on the Saffir–Simpson hurricane scale. The first system, an unnamed tropical storm, developed during the month of June in the southern Gulf of Mexico. The storm moved northward across Central America, but caused no known impact in the region. It struck the Florida Panhandle and caused minor impact across much of the Southern United States. Tropical cyclogenesis halted for over two months, until Anna formed on August 21. The storm remained well away from land in the far North Atlantic Ocean and caused no impact.