Friend, 28, was withdrawn during the 1-0 defeat by Nottingham Forest on 23 January after landing awkwardly.
Former Doncaster and Wolves full-back Friend has missed just one league game this season, scoring once.
Boro are already without centre-back Ben Gibson with a hip injury, who can also play wide, while full-back James Husband is on loan at Huddersfield.
Middlesbrough defender George Friend will be out for approximately four weeks after fracturing a shoulder.