The former Celtic star is set to be sidelined for at least two weeks with the problem after just returning from a hernia injury.
The 26-year old was forced out of Boro's 2-0 home win over Preston North End on Tuesday night and is expected to miss upcoming fixtures against Watford (away), Crystal Palace (home) and Plymouth Argyle (away).
"Scott's got a hamstring problem," confirmed Boro boss Gordon Strachan. "It's enough to keep him out for a couple of weeks I think. I'll add that to the other injuries."
McDonald has scored just one goal in seven appearances since joining the Teessiders in January.