"We've played many times and it is always super tough and super exciting".
Barty, the Australian 12th seed, was in fine form as she brushed past wildcard Jennifer Brady 6-3 6-2, setting up a meeting with Svitolina.
"Before the match I did not feel great and then it just got worse with every second - extreme dizziness and extreme fatigue", the American said in a statement.
"I don't really play that often, so when I do, I need to play well", she said.
Williams led 3-0 in the first set before momentum flipped decisively in favor of her fellow former world No. 1, with Muguruza storming back with six unanswered games to take the set 6-3.
"By the score it might have looked like I started well, but I was not feeling at all well physically".
Coming into Indian Wells as the WTA's 10th-ranked player, she lost power on her serve and did not appear to be moving with her usual agility.
"It was really hard against her because I never played against her - it was a bit hard to get a rhythm", Halep said.
Williams, 37, had shown signs of fatigue during the first set and after it was completed she called for a trainer and following a lengthy conversation returned to the court.
She is now ranked 10th in the world.
"I never played her, so it's also you're out there learning", Williams said.
It's the second time in four years that Williams has withdrawn from the tournament. In the victory, Venus won 59 percent of her first serve points and 52 percent of her second serve points.
"It was hard for me to close those sets, but I'm actually proud that I could do that", added the Romanian.
Two seeded women lost: No. 11 Anastasija Sevastova, who retired trailing 5-0 in the first set against No. 21 Anett Kontaveit, and No. 15 Julia Goerges, who lost to Mona Barthel 7-5, 1-6, 6-4.