Versatile back Daly scored twice in a 21-3 Champions Cup win over La Rochelle last weekend, but was forced off in the second half, while Hughes and fly-half Jimmy Gopperth were also injured in the contest.
All three men were sent for scans this week but none of the trio will require surgery.
Daly, though, is expected to miss between 10 and 12 weeks of action, while Hughes is due to be sidelined for between eight and 10 weeks.
England begin the defence of their Six Nations title with a trip to Italy on February 4 before welcoming Wales to Twickenham six days later.
If number eight Hughes can recover quickly enough, he may be in contention to face Scotland in round three at the end of that month, but Daly's initial prognosis means the Calcutta Cup clash is likely to come too soon.
Photo Getty Images. Caption: England back Elliot Daly