In the other semifinal, 2006 winner Maria Sharapova will face fellow Russian Maria Kirilenko.
Another Russian, 18th seed Maria Kirilenko, suffered a surprise 6-3 6-1 defeat by Iveta Benesova of the Czech Republic.
Azarenka beat Maria Kirilenko of Russia 6-3 6-4 in the battle for bronze.
Among the seeded women to lose were No. 6 Angelique Kerber, No. 11 Nadia Petrova and No. 14 Maria Kirilenko.
Sharapova will next face 21st-seeded Czech Klara Zakopalova, who upset another Russian when she beat No. 14 Maria Kirilenko 6-2 7-6 (7-4).
Then Maria Kirilenko came back to beat Petra Kvitova in three sets.
Denmark's Caroline Wozniacki eased past Urszula Radwanska 6-1 6-2, while there were also wins for Russia duo Maria Kirilenko and Ekaterina Makarova.
Elsewhere, sixth seed Anna Chakvetadze set up an enticing third round meeting with fellow Russian Maria Kirilenko by beating Alisa Kleybanova 6-3 6-4.
In the women's side of the tournament, World No.1 Serena Williams cruised into the last eight with 6-3 6-1 win over Maria Kirilenko.
The American, who defeated Timea Bacsinszky of Switzerland in her opening match on Tuesday after a first-round bye, will next face Maria Kirilenko.
Maria Kirilenko, at 13th the highest-ranked player in the first-round tie, won the opening singles rubber 7-6 (7-3) 6-4 against 42-year-old Kimiko Date-Krumm.
She had to retire in the fourth round of the Australian Open in the first set of her clash with another Russian, Maria Kirilenko.
Sharapova's semifinal opponent will be countrywoman Maria Kirilenko, after the 13th seed upset in-form world No. 8 Petra Kvitova with a 4-6 6-4 6-3 win.
Russian seeds Svetlana Kuznetsova, Anastasia Pavlyuchenkova and Maria Kirilenko also went through, with the latter to face Canada's Aleksandra Wozniak after eliminating Australia's Jarmila Gajdosova.
Henin will now face China's Zheng Jie who cruised into the last four with a straight sets - 6-1 6-3 - victory over Russia's Maria Kirilenko.
Second seed Caroline Wozniacki came from behind to defeat Bulgarian qualifier Tsvetana Pironkova 3-6 6-3 6-4 and set up a third-round tie with Russia's Maria Kirilenko.
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The teenager had only got to bed at 1am after losing her doubles quarter-final alongside Sally Peers against Maria Kirilenko and Agnieszka Radwanska late on Wednesday evening.
But the 22-year-old shut out the distraction to triumph 6-0 3-6 6-1 in a see-saw match against Russia's Maria Kirilenko -- securing a last four place against Wickmayer.
Russian No. 2 Sharapova will play 20th-seeded compatriot Maria Kirilenko, while the remaining quarterfinal tie pits China's French Open champion Li Na against German No. 18 Angelique Kerber.
Russia's Maria Kirilenko beat eighth-seeded compatriot Elena Bovina 6-3 6-1.
World No. 2 Dinara Safina cruised into the fourth round with a 6-1 6-2 win over unseeded Elena Baltacha of Britain, and will next play fellow Russian Maria Kirilenko.
Dominika Cibulkova beat Anastasia Pavlyuchenkova 5-7 6-1 6-4, and then Daniela Hantuchova defeated Maria Kirilenko 6-2 6-4 as the Slovakians seek to reach their first final since winning the 2002 title.
Second seed Safina, beaten in last year's final by Serena Williams, suffered a worrying recurrence of an old back injury as she retired trailing 4-5 in the first set to compatriot Maria Kirilenko.
In the absence of world No.2 Sharapova and 10th-ranked Zvonareva, Russian captain Shamil Tarpishchev has turned to two-time grand slam champion Svetlana Kuznetsova, as well as Anastasia Pavlyuchenkova, Maria Kirilenko and Elena Vesnina.
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Serena Williams, playing her first tournament since winning the year's opening Grand Slam, the Australian Open in late January, had her easiest win of the week as she dispatched Russia's Maria Kirilenko 6-1 6-4.
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Russia's Maria Kirilenko won her sixth title by edging German fifth seed Sabine Lisicki 5-7 6-1 7-6 (7-1) at the Pattaya Open , having lost in the final of the Thai event last year.
Second seed Caroline Wozniacki is also through, although the Dane had to fight back from a dismal opening set to defeat Maria Kirilenko 1-6 6-1 6-4, while seventh seed Jelena Jankovic was another women's seed to progress.
Former French Open winner Li Na overcame Chinese compatriot Zheng Jie 6-3 6-1 as she bounced back from her first-round defeat in Madrid, while there were also victories for Samantha Stosur, Maria Kirilenko and home favorite Roberta Vinci.
Later Tuesday, China's Zheng Jie -- the first female tennis play from the Asian giant to make it into the quarterfinals -- will face unseeded Maria Kirilenko, who put out former champion Maria Sharapova in the first round.
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