The South Africa international made just nine top-flight appearances in 2014-15 as a knee injury badly hampered his campaign, and sat out Sunday's game at Hearts after suffering an issue in training.
Roberto Martinez confirmed Pienaar would be unavailable for Everton's season opener against Watford on August 8 as he instead starts work on his rehabilitation.
"Obviously it was a really sad moment for all of us when Stevie picked up that injury in training," he told the club's official website.
"He's gone back now to be fully assessed by our medical team at Finch Farm and we'll get the results very soon.
"But it does seem it's a problem with his hamstring and clearly he's going to miss the start of the season, which is a real shame because Stevie worked with fantastic results and fantastic signs over the first three weeks or pre-season.
"We were very, very down about that situation and we hope to get Stevie back as soon as we can."