The defender went off after just 13 minutes of the game against Stoke on Saturday after he pulled a hamstring early in proceedings with Howe having to rearrange things in the side.
Cook is set for a scan this week and his absence adds to a defensive problem for the Cherries.
Howe told reporters: "He felt his hamstring on one of the passes he made wide and we knew instantly he couldn't continue.
"With our stretched resources defensively, it is a big blow for us.
"Full credit to Ryan Fraser for playing at right-back. It is one thing playing wing-back, that's quite like his normal role as he played at Chelsea.
"Although moving deeper to play right-back is not new to him, he hasn't done it so much in the Premier League. I thought he handled himself very well."