The fire has been extinguished and there are no injuries.
The spokesman for the government of Guerrero state says four men entered the hotel before dawn Monday, asking for a person they apparently believed was staying there.
Spokesman Arturo Martinez says the men started setting the fire after hotel employees refused to give them information.
The Hotel Costa Linda is located in an old part of Acapulco that is not much frequented by foreign tourists.
The Pacific coast resort has seen a wave of crime and drug-gang violence in recent years.
(Copyright 2012 by The Associated Press. All Rights Reserved.)