The England U21 international was forced to withdraw from the European Championship in the Czech Republic after suffering a knee injury during training ahead of their opening game against Portugal.
The England medical team put the striker through tests to assess the full extent of his ligament injury and scans show the problem is not as serious as first feared.
West Brom’s performance director Dr Mark Gillett told the club’s website: “Saido has got a ligamentous tear of his knee which does not require surgery but careful rehabilitation for up to four weeks.
“We are grateful to the England medical staff for putting Saido’s welfare first.”
West Brom kick off the new season with a home match against Manchester City on Saturday, August 8. Click here for their fixtures for the 2015/16 season.