Baggage handler Swissport is holding the items at the facility as they work through a large backlog.
It comes the aviation industry is suffering major disruption as a surge in demand for travel coincides with staff shortages across roles such as airline crew, ground handlers, airport security staff and air traffic controllers.
Thousands of flights have been cancelled and many passengers have been forced to wait for several hours in long queues at airports across the United Kingdom.
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Dammy Akinyemi, from Livingston, is still waiting for her luggage to be returned two weeks after a holiday to Canada.
She told the BBC she trawled through hundreds of bags and suitcases at the Swissport warehouse.
"I was there for four hours in this unit, I looked through every single bag," she said.
"There was only three staff handling thousands of bags, and they couldn't give me any information. All they would say is, 'if it turns up we'll let you know'.
"It really upsetting because I've got personal, family stuff in the bag that I can't replace."
Swissport told the BBC bags are processed as soon as they arrive at Edinburgh Airport – but a backlog has built up.
A spokesperson for Swissport said: “Unfortunately, a significant number of bags from a range of airports and operators are not being loaded onto connecting flights into Edinburgh.
“Instead, they are arriving on different, later flights after most passengers have already left the airport. The knock-on effect of these missed baggage connections has created a backlog of luggage to be processed.
“We understand this is a really frustrating situation for passengers and we're working closely with our airline and airport partners to process these bags as fast as we can.”
Edinburgh Airport has urged passengers to contact their airline or handling agent for missing luggage issues.
A spokesperson said: “This is a challenging time for the entire aviation industry and we know airlines and handling agents have been working hard to reunite passengers with their baggage.
"We're doing what we can to support them in this, and this includes access to secure designated storage areas on campus which is now allowing them to process items and repatriate them with their customers.”