The midfielder missed the 5-0 home victory over League One side Brentford in the Capital One Cup on Tuesday night after hobbling off in the league win at Yeovil at the weekend.
The 21-year-old will remain on the sidelines when the Rams resume Championship action against Burnley on Saturday and he is unlikely to go on international duty with the Republic of Ireland next week.
Hendrick, who has had a scan but may need further tests to discover the full extent of the problem, will see a specialist on Friday.
"He won't be any good for Saturday but we hope it is not too long after that but we will get that confirmed towards the weekend," said Derby boss Nigel Clough.
"He is still in a bit of pain and hobbling around on crutches.
"We will miss him on Saturday and we missed him against Brentford but Paul Coutts and John Eustace came in and deputised well."