The influential Belgium international defender is still recovering after suffering a tweak in the same hamstring which kept him sidelined for four months earlier this season.
And while Mauricio Pochettino is keen to get him back in the side as quickly as possible, it is very unlikely that he will face the Terriers or Juve at Wembley in the coming week.
However, the Argentinian, who is celebrating his 46th birthday on Friday, could be boosted by the return of Alderweireld's defensive partner, Jan Vertonghen, from an ankle problem.
Pochettino said: "We need to be cautious with him [Alderweireld]. I think still we need to assess every day.
"I don't believe he can be ready for Juventus. But, yes, happy because Jan is back again and maybe he is available for tomorrow to play."
Pochettino also rejected the possibility of resting some key players for the clash against the Terriers, with one eye on Wednesday's Champions League last-16, second-leg clash against Juve, with the tie finely poised at 1-1.
He added: "No, both our eyes are focused on the game against Huddersfield. That for us is the most important game.
"It's an important three points for the battle for the top four. We cannot think of the game after.
"We need to be focused and ready to compete because it will be tough. Huddersfield are in a position where they need points, too."