Striker Goulding suffered a dead leg just seven minutes into the Cherries' 2-1 pre-season defeat against Phil Parkinson's side.
Howe's squad is already down to the bare bones and he is unable to strengthen due to a Football League transfer embargo.
Howe told the club's official website: "We lost Jeff to a dead leg and I don't know how long he'll be out for and if he isn't fit, it will leave us short up front which is a bit of a worry.
"Any injuries we pick up now will hurt us because it is a small squad. Alan Connell has started training, but he is a long way behind in terms of match fitness."