The theft of the items from the island's community shop has attracted huge media attention from across the globe.
Crime is so rare on the island, it's thought that there hasn't been a recorded case of theft since the 1960s.
"We are overwhelmed by the generosity and support of people from all over the world, who've offered donations and offered money," said one resident, who didn't want to be named. "We've had calls from Australia and America -- it's incredible.
"The police were here; they're doing their investigation, and we're hoping we'll get somewhere," he said. "We just want to get the hats back."
Hand-knitted hats were 'unique'
The manager of the community shop, Julie McCabe, put many hours of effort into making the unique hand-knitted Canna wool hats that were stolen.
The island, just five miles long and one mile wide, is 30 miles from the Scottish mainland and is owned by National Trust Scotland.
Its shop is run on a voluntary basis -- with an honesty box for customers who stop by when the shop isn't manned.
Traditionally, it has been left unlocked and open to visitors through the night.
However -- in a sign that the crime might have changed life forever on the island -- it may now be locked.
"We left it open specifically to welcome fisherman in to use the Wi-Fi and buy anything they needed while resting at our pier overnight," a post on the island's community Facebook page said.
"The feedback from the fishing community was that it is a most welcome service. It is therefore very sad that they and other visitors have to lose out."
Police Scotland said an officer had been sent to the island on Wednesday to follow up on any leads.
A spokeswoman said inquiries were ongoing.
The theft took place sometime between 8 p.m. last Friday night, and 8 a.m. Saturday morning local time.
Police said they want to speak to members of the public and those on board fishing vessels which were moored at Canna Pier at the time of the theft.
Such incidents 'very rare'
"It is extremely disappointing that the Isle of Canna Community Shop has been targeted by opportunistic thieves who have taken advantage of this rural community's trusting nature," said Community Policing Inspector David Campbell.
"Such incidents are very rare in Canna."