Ward was included in Michael O'Neill's 24-man squad despite not having played for his club since September 30.
Rams boss Nigel Clough told reporters: "He won't be fit - I can understand they want him but firstly he has to be fit for us."
He added: "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 by confirming the 26-year-old's withdrawal, with a brief statement that read: "Jamie has been ruled out of Northern Ireland's World Cup Qualifier against Azerbaijan next week as a result of a hamstring injury."
No replacement has been named.