The France international tore the anterior cruciate ligament in his left knee in training on Tuesday and is expected to be out for eight to nine months. Diaby has struggled with repeated injury problems ever since joining the Gunners in 2005 but Wenger has urged him not to give up after his latest setback.
"I hope he will not give up and will continue," the French manager told reporters. "When you look at the number of problems he had, the surgeries, he is 26 years old and has had four or five big surgeries. That demands a lot of mental strength to come back."
The 26-year-old has made just 14 appearances this season and has previously endured long-term absences brought on by ankle and thigh injuries. Fellow midfielder Jack Wilshere is also currently sidelined with an ankle problem and Wenger expressed his surprise at the severity of the Diaby's damage.
"I thought originally it was just a little twist of the knee," he explained. "When they told me it was a rupture of his cruciate, and when you know what this guy has gone through, how many times he has worked day and night to come back in rehab, it is just demoralizing.
"I hope he will find the resources and the strength to fight for a comeback because he was quite down."