The man's son, who was also singing with his father, was seriously wounded in the attack at the Long Horn Saloon in Ao Nang, a coastal resort town.
The dead man has been named as Bobby Carter, 51, and his son is Adam Hayes Carter, 27.
Three men are under arrest for the murder, say police.
The killing took place when three local men objected to the Carters hogging singing time at the saloon about 1am today, officers said.
The dead man and his son were taken to Krabi Hospital and the son was transferred to Bangkok Phuket Hospital in Phuket, a neighboring province also noted for tourism, early today.
Three men have been arrested for stabbing the two American with sharpened steel rods, a preferred local weapon.
The three men are Ratikorn Ramin, 27, Sathit Somsa, 40, and Noppanan Yoddecha, 26. They are being held in Krabi.
Adam Carter declined a request for an interview today. He appeared to be in reasonable condition and able to talk when reporters called at his room.
It's believed the stabbing took place out the front of the saloon.
The killing is bound to reignite the issue of tourist safety in Thailand. Police are using more security cameras on Phuket and have introduced ''Safety Zones'' in key tourist areas, including the nightlife hub of Patong, on the west coast.
Krabi is further off the beaten tourism track and not as much attention has been paid to safety there. The best-known destination in Krabi is the offshore 20-something rites-of-passage island of Phi Phi.
Krabi has been the scene of several violent crimes against tourists in the past 18 months, including the unprovoked knife attack on a British man strolling home with his girlfriend.
A German woman had a thumb cut off in another attack.
The notorious rape of a Dutch tourist in Krabi triggered her father to pen and sing a viral YouTube song about justice and revenge, 'Evil Man from Krabi.'