Ivanovic needed just 27 minutes to win the first set for the loss of one game as she capitalised on Koukalova's weak second serve.
The second set was a more even affair with the Czech momentarily leading 4-3 before Ivanovic reeled off the final three games to set up a semi-final with Shuai.
The Serbian has yet to drop a set in her three matches in the grasscourt tournament.
"I really tried to do my thing because I know she can be dangerous and last time we played, in Doha, I lost," Ivanovic said. "She's won on grass in the past and is a great competitor as she showed in her matches this week.
"I expected a tough match so from the first moment on I was trying to be really aggressive. I tried to dominate her and put pressure on her and I played really well in that first set.
"The second set was a lot tougher. She's a tough competitor. I'm really happy to win in two sets," said Ivanovic.
The other semi-final pits Strycova against Australian Casey Dellacqua who beat 43-year-old Japanese Kimiko Date-Krumm 6-1 6-0.
(Reporting by Tom Hayward, editing by Tony Jimenez)
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