The animal welfare charity was alerted after a runner in Glasgow Green saw the pup and raised the alarm on Saturday July 15.
Inspector Elaine Lindsay said, “We are very lucky the puppy was seen, as she was hiding under a cardboard box and was difficult to spot under all the rubbish in the skip.
“She’s a black terrier cross type dog, around 5 to 6 months old and in good condition despite the distress of being left in the skip.
“Staff at the centre have named her Skippy.
“Skippy has been well fed, but also has her tail docked so we’re keen to speak to anyone who may be able to help us establish why she was left here in the first place.”
Abandoning an animal is an offence under the Animal Health and Welfare (Scotland) Act 2006.
Anyone found guilty of doing faces being banned from keeping animals for a fixed period of time or for life.
Anyone with information is urged to contact the charity’s animal helpline on 03000 999 999.