Willock, who has already missed large parts of the season due to Achilles and hamstring injuries, limped off in the first half of Newcastle's 1-0 victory over Fulham at Craven Cottage last week.
Newcastle will be hoping it is not a long-term injury for Willock, with Jamaal Lascelles, Nick Pope, Kieran Trippier and Callum Wilson among a lengthy list of players already sidelined.
"Joe's been to see another specialist to check on the progress of his Achilles. It's been problematic for him," Howe told reporters.
"It has been a difficult injury, it has not been straightforward because he's had a few complications through the process. The feedback was generally positive, in the respect that the Achilles is healing and doing well.
"But it will fluctuate from time to time and he will have moments where it is not feeling so good. For Tottenham, I probably think he won't be available.
"There's a chance he will then be available through the rest of the season but, again, that's slightly unclear. We need to make sure the long-term prognosis for him is positive, and that might mean a short period of rest."
Howe said the player closest to making a return from injury was defender Tino Livramento, adding: "He has not trained with the team but has been out on the grass.
"Lewis Hall has not trained at all this week, so he is a slight concern from last week.
"Other players are doing well in the background so I am hoping in the not-too-distant future we can get three or four back."
Newcastle are in eighth spot, 13 points behind fourth-placed Spurs, who they beat 6-1 at home last season.
"I admire them tactically; I admire them physically," Howe said. "A lot of credit must go to (manager) Ange (Postecoglou) for the job he has done and the philosophy he has implemented. I think they have played very well this year."
