The airlines has written to the communications ministry and multimedia commission and also lodged a police complaint about the circulation of these messages on blogs and Twitter and Facebook postings.
AirAsia operates many flights to Indian cities.
'We advise the public to disregard malicious messages circulating on Twitter, Facebook or via chain SMS. We will not hesitate to take strong legal action and initiate civil or criminal proceedings against individuals or groups who circulate or spread false and malicious messages regarding our company, particularly relating to matters of safety,' AirAsia said in a statement.
The company headed by an ethnic Indian, Tony Fernandes, said it would do all it could to trace those responsible for spreading the messages.
Hoax messages about an AirAsia flight having crashed Sunday spread like wildfire through text messages and the social networks.
According to the messages, the flight had crashed at the Kuching airport in Sarawak state or at the Kuala Lumpur International Airport.
AirAsia said the rumours had caused panic among the public and disrupted its operations.