According to a press release by the England and Wales Cricket Board, the 24-year-old went through scans on his injured right elbow, which confirmed a low grade stress fracture.
"He will now commence an injury rehabilitation programme with the ECB medical team with a view to be ready for the international summer campaign starting in June against the West Indies in a three-match Test series," ECB said.
Archer, who made his debut for England last year, could only take part in one Test on the tour of South Africa.
England won the Test series against South Africa 3-1. They are now playing a three-match ODI series against South Africa before heading to the T20I series.
England are scheduled to play two Tests in Sri Lanka starting March 19.