The 24-year-old, who has scored nine goals already this season, limped out of training with the problem.
Liverpool's medical team are still assessing the extent of the problem but the England international will not be fit for the trip to the KC Stadium.
Sturridge's injury could not have been more unfortunately timed after manager Brendan Rodgers praised his attitude in training over the last week after dropping the forward for last weekend's Merseyside derby.
The Reds boss felt the player, who had been affected by a dead leg for a couple of weeks, was not fully fit after 90 minutes for England in the friendly against Germany.
However, he was pleased with the reaction Sturridge's omission against Everton had provoked.
"Players will react differently. You will find some players, if they are not in the team, they just shrivel and die and have no fight," he said.
"The top players when they don't play they show you every single day what they can do and that has been the case this week.
"He has certainly trained very hard this week. He has been really determined, strong and aggressive and he looks ready for the weekend.
"He has worked exceptionally well and when he does that his quality is there for all to see."
The club later confirmed Sturridge's injury. "Daniel Sturridge will be assessed by the club's medical staff today after the striker rolled his ankle in training," said a statement on liverpoolfc.com.
"Sturridge returned to training at Melwood this week; however, he sustained an ankle sprain which will require further assessment."
You can watch Liverpool's clash with Hull City live on Sky Sports 1HD on Sunday from 1pm.