The Catalan giants confirmed on Friday that the 22-year-old goalkeeper will miss the start of the season, with tests having revealed the extent of the back injury he sustained on Monday.
Having arrived at Camp Nou during the close-season on a free transfer after his contract at Borussia Monchengladbach expired, Ter Stegen is viewed as the long-term replacement for Victor Valdes.
However, his injury means fellow newcomer Claudio Bravo is likely to start in goal when Barca open their Liga campaign against Elche next Sunday.
A Barca statement read: "The first team goalkeeper Marc-Andre ter Stegen, following persistent pain in his lower back caused by a blow received in training last Monday, August 11, has been subjected to new medical tests this morning which have revealed the existence of a small fracture in the transverse apophysis of vertebra L3.
"The club's medical services reported that the player will be out for between two and three weeks. The player will carry out recovery work during this period.
Ter Stegen made his first appearance for Barca in a friendly against Recreativo Huelva last month and started the 1-1 draw with Nice on August 2.