Jennings, who was listed as questionable on Friday, injured his left thumb in Week 2 against the New Orleans Saints.
He wore a small cast during practice this week and was expected to remain the Giants' starter this week against the Redskins.
"(Jennings) is a veteran back. He's played a lot of football in this league," coach Ben McAdoo said Friday. "He's earned his spot. And yeah, I'm comfortable with it."