The Scottish SPCA was alerted on Monday after the rodent was discovered at Cardonald Cemetery by a dog walker.
The hamster is now in the care of the Scottish SPCA's Glasgow Animal Rescue and Rehoming Centre in Cardonald, where he has been named Java.
Animal Rescue Officer Emma Campbell, said: "Java was discovered by a man who was walking his dog through the cemetery when he spotted the coffee jar with the poor wee guy inside.
"Java is a very friendly hamster and it's clear he's used to being handled. When he arrived in our care he was a bit straggly and had a sore eye, however, his eye is being bathed daily and is already looking a lot better.
"Abandoning Java was an extremely cruel thing to do and he would have eventually starved to death had he not been found in time.
"Java is now looking to find his new forever home where he can be loved and cared for properly."
Anyone with information on Java is being urged to contact the Scottish SPCA Animal Helpline on 03000 999 999.
Abandoning an animal is an offence under the Animal Health and Welfare (Scotland) Act 2006 and anyone found guilty of doing so can expect to be banned from keeping animals for a fixed period or life.