"It would be such a terrible thing to lose physical books," he told BBC News.
"That's the direction we're heading in because publishers are not responding as effectively as they ought to."
The "solution to the industry's malaise" is to give buyers a free download code when they buy a printed book, he said.
His comments come weeks after Amazon announced a plan to offer buyers of printed books in the US a free or discounted digital version. Similar schemes have been rolled out for magazines and music.
"If they [publishers] don't move to that really quickly people will be forced to take the digital version whether they really want to or not," Bryson said.
"Somebody gave me a digital reader as a gift last spring and I now find that when I'm travelling I take digital books with me.
"I'm being forced into that and I kind of resent it."
Bryson was speaking at the Booksellers Association conference ahead of the publication of his latest book, One Summer: America 1927.