The Times of India reported the chief airport security officer received the letter that also said the plane could be en route to New Delhi or another Indian city.
The letter did not give details, such as the name of an airline.
The security alert came a day after the Indian Parliament approved a highly controversial bill to split Andhra Pradesh creating India's 29th state, Telangana.
Creation of the state would end a decades-long battle by ethnic Telangana people, who speak Telugu, to have their own state.
At the heart of the dispute is Hyderabad, India's sixth-biggest city and a magnet for IT research and pharmaceutical investment dollars.
The Hyderabad region is home to most of the Andhra Pradesh's important schools and universities.