The Baggies striker was forced out of the England squad on the eve of their European Under 21 Championships opener against Portugal after suffering an injury in training.
Berahino has since undergone further examinations to assess the full extent of the injury, but these have revealed no major damage to his right knee.
West Brom’s performance director Dr Mark Gillett said: "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."
Berahino should be ready for the opening game of Albion's Premier League campaign when they welcome Manchester City to the Hawthorns on Saturday 9 August.