A 20-day-old baby sleeping on a mattress survived when she floated to safety after Penang island was hit by killer tidal waves, local media reported on Tuesday.

S Tulasi was sleeping in a room behind her father's food stall on Penang's popular Batu Ferringhi beach when the waves hit.

"We were all caught off guard. I was thrown several metres away but managed to hold onto one of the posts," A Suppiah, 55, was quoted as saying by the Bernama news agency.

His wife, Annal Mary, 40, fought her way through the swirling waters to the room where the baby was sleeping.

"Thank God the mattress was floating in about 1.5 metres of water and my baby was crying," said Suppiah.

According to official police figures, at least 60 people have been killed and nearly 200 injured in Malaysia by huge tidal waves triggered by a massive earthquake off the Indonesian coast.