Romanian Halep was trailing 2-6 6-3 1-0 when she withdrew saying she "had a headache" and "felt sick".
In the men's event, Kei Nishikori beat Tommy Paul 3-6 7-6 (10-8) 6-4 to set up a semi-final against Alexander Zverev.
Canada's Milos Raonic lost 7-5 6-4 to American Jack Sock, who will play Kevin Anderson in the other semi-final.
South Africa's Anderson, who knocked out Austrian top seed Dominic Thiem, hit 21 aces to defeat 200th-ranked Indian qualifier Yuki Bhambri 6-4 4-6 6-3.
World number 10 Raonic's exit means he has now gone 30 tournaments since lifting his last trophy in Brisbane in 2016 - a drought of 19 months.
Japan's Nishikori saved three match points against American Paul in a contest which lasted two hours and 40 minutes, compared to German Zverev's 57-minute 6-2 6-4 win over Russia's Daniil Medvedev.
Next up for Makarova in the women's draw is a semi-final on Saturday against French fifth seed Oceane Dodin, who beat Germany's Sabine Lisicki 5-7 6-4 7-6 (7-4).
The other women's semi-final will be an all-German tie as fourth seed Julia Goerges, who beat Monica Niculescu 6-3 6-4, takes on unseeded Andrea Petkovic following her 6-7 (3-7) 6-1 6-2 victory over Bianca Andreescu.
Meanwhile, in the Stanford Bank of the West Classic in California, Wimbledon champion Garbine Muguruza reached the semi-finals with a 6-1 6-3 win over Croatia's Ana Konjuh.
However, two-time Wimbledon champion Petra Kvitova was comprehensively beaten 6-2 6-0 by 18-year-old American Catherine Bellis.
Kvitova, who only returned to tennis in May after a knife attack that threatened her career, hit 26 unforced errors in the match.
The semi-final line-ups will see Bellis, 18, take on compatriot Coco Vandeweghe, while Muguruza faces American Madison Keys, who beat Lesia Tsurenko, of Ukraine, 6-4 6-3.
World number two Simona Halep was forced to retire from her Washington Open quarter-final against Ekaterina Makarova with a heat-related illness.