With Halep leading 3-2, umpire Kader Nouni jumped from his chair to alert security officials to the woman's illness and told both players to go to their sideline chairs.
Temperatures on Centre Court were 77 F (25 C) under sunny skies.
Following a delay of four minutes and after the woman was taken away by medical staff, the tiebreaker resumed. Bouchard won it 7-5 to take a one-set lead.
The match was also delayed for five minutes at the end of the fourth game when Halep injured her left ankle and needed a medical timeout to have it taped.