Scotland's Menzies appeared dizzy by the oche while leading 2-1 before being led off stage at the Winter Gardens.
The 37-year-old received medical attention but was not cleared to continue playing, leading to the match being abandoned.
"Cameron experienced high blood pressure, which caused him to feel dizzy and subsequently faint," a statement from the PDC read.
"Following an assessment by the on-site medical team, Cameron was deemed well enough to return to his accommodation.
"We wish Cameron all the best and look forward to seeing him back in action soon."
Smith advances to the quarter-finals where he will face Gerwyn Price after the Welshman knocked out Rob Cross 11-5.
'The Iceman' surged into an 8-3 lead after a loose opening set of legs and dealt with a brief mid-match wobble to close out the victory.
"I felt like I was struggling all through the game," Price admitted to Sky Sports.
"I couldn't find my scoring game, it was up and down.
"If I want to win this tournament I need to be a lot better than that, but I am going in the right direction."
World number three Gian van Veen progressed to the last eight by overcoming fellow Dutchman Wessel Nijman in a thrilling 14-12 tie-break.
Van Veen broke twice early on, including a 135 checkout before Nijman took out 116 en route to drawing level at 5-5.
The pair exchanged blows and Nijman edged ahead 10-9 to lead for the first time since leg one, but the clash was heading down to the wire.
Van Veen kept himself in the tie with a huge 148 checkout to make it 11-11 with Nijman down on 64 against the throw.
Van Veen grabbed the all-important break of throw in the 25th leg before eventually seeing out the match.
James Wade won the night's final match and will play Van Veen in the quarter-finals after seeing off Ryan Searle 11-8.
Wade's 121 checkout moved him 7-5 ahead in a contest that saw him slightly ahead all match.
'The Machine' hit a 143 out to break Searle's throw, then consolidated to make it 10-7 before ensuring his progress.
Wednesday's World Matchplay results
Cameron Menzies 2-1 Ross Smith - Smith wins by walkover
Gian van Veen 14-12 Wessel Nijman