"As soon as we came into the hotel we could see something was wrong and money had been taken. It is quite sad."
The community trust-owned hotel is leased by a private business. The island hit headlines in 2002 when it was the subject of a community land buyout.
Resident Willie McSporran, 82, who led the island's community land buyout in 2002, said: "It's terrible that these things are happening now after all these years.
"The last thing I remember is a bike going missing about 20 years ago, when my brother had the local shop."
Alastair Redman, ward councillor for Kintyre and the Islands, said: "On Gigha, much like most of our island communities, there is no crime.
"How someone could steal from not only a private business in a small beautiful place like Gigha I don't know, but to steal from the community trust is absolutely unfathomable.
"If residents need any help to try to find out who is responsible I would be happy to lend my support.
"This is really shocking. Theft and rural crime seems to be on the increase. This is the exception to the rule. However it can't be ignored by the local constabulary and I hope they take it all the way."
A Police Scotland spokesman said: "Between 10pm on Saturday, September 8, and 1am on Sunday, September 9, at the Gigha Hotel on the Isle of Gigha, entry was gained to a store room and money was stolen.
"Constable David Hope at Campbeltown Police Station is investigating and is appealing for witnesses or anyone with any information to contact him on 101 or anonymously through Crimestoppers on 0800 555 111."