Norrie pulled out with illness, according to the ATP, which did not provide further details.
The Brit, who is chasing a spot in the season-ending ATP Finals, had powered his way through the round of 16, beating Kaichi Uchida (28) 6-2 6-2 to comfortably advance.
Speaking after that game, Norrie said he was struggling with jetlag but was looking forward to the quarterfinals.
Norrie is the third seeded player to withdraw from the Korea Open in Seoul, after sixth seed Borna Coric (25) dropped out on Monday and third seed Taylor Fritz (24) withdrew on Thursday.
World number two Casper Ruud (23) remains in the tournament as the top seed, as does fourth seed Denis Shapovalov (23) and eighth seed Brooksby.
The American will face Shapovalov in the semi-final on Saturday.
