The 26-year-old was forced to end her 2013 season in August due to the problem but beat Estonia’s Kaia Kanepi 4-6 6-3 6-2 to reach the last four.
Top seed Williams, meanwhile, overcame ninth seed Dominika Cibulkova 6-3 6-3 in her quarter-final.
“I think I got to win a few times in order to call it rivalry,” said Sharapova when asked about the prospect of facing Williams.
“I haven’t had a lot of success against her in the past.
“It’s the first tournament of the year. I came here wanting to play as many matches as I could and obviously wanting to play the best.”
Jelena Jankovic will take on Victoria Azarenka in the other semi-final after the Serb overcame Angelique Kerber 6-7(8) 6-3 6-1. Second seed Azarenka, meanwhile, battled past Stefanie Voegele 6-4 6-7(7) 6-1.