The 29-year-old, who is on loan at Oakwell from Crystal Palace, suffered a thigh injury during Saturday's 2-0 defeat at his former club QPR.
Ramage underwent a scan on Monday and the news was not good.
He wrote on Twitter: "Scan yday and not as good as hoped, looks like several weeks on sidelines. Day1 of rehab and shall be doing everything to get back quick!"
Ramage has made five appearances for the Tykes since joining in September.