The woman, believed to be in her 60s, donated electronic items to CleanBayArea in Milpitas, California, in April.
Included in the boxes of computer parts was a 1976 Apple-1, the recycling company's vice president Victor Gichun told NBC News.
"We thought it was fake. It was real," he said.
Mr Gichun said the woman told staff at the recycling centre that she found the parts while cleaning out her garage after her husband died.
She did not leave her name nor fill out a tax receipt for the donations, he said.
Mr Gichun is hoping to find the woman to give her a $100,000 cheque - half of what the computer fetched in a private auction.
The recycler's policy is to split the proceeds with the person who donated the equipment.
"Tell this lady to please come over to our warehouse in Milpitas again," Mr Gichun said.
The Apple-1 was one of the tech giant's first pre-assembled computers.
They were first manufactured by Steve Wozniak in the garage of Apple co-founder Steve Jobs.
The original units retailed at $666.66 - the equivalent of around $2,786 (£1,821) in today's prices.
Only a few dozen of the groundbreaking home computers are known to still exist.
An Apple-1 in near mint condition sold at auction in New York last October for a record $905,000 (£564,000).