Ward was included in Michael O'Neill's 24-man squad despite not playing for his club since September 30, and the Rams' boss said that a return to the international fold is highly unlikely.
"He won't be fit - I can understand they want him but firstly he has to be fit for us," Clough told reporters.
"He's not looking like he'll be back this week, so it would be difficult for him to make next week's international."
The Irish Football Association followed up Clough's comments by confirming the 26-year-old would be withdrawing from the squad. In a statement, the IFA said: "Jamie has been ruled out of Northern Ireland's World Cup Qualifier against Azerbaijan next week as a result of a hamstring injury."
A replacement has yet to be named.