Midfielder Wilshere missed Arsenal's 2-0 win over Liverpool on Saturday due to an ankle problem, while Gibbs was substituted after 78 minutes with a calf injury.
"Jack has an inflamed ankle," Wenger told reporters. "Will he be available for Wednesday? I do not know.
"We will have to wait until Monday to see. Gibbs has a calf problem. I don't know exactly how bad it is."
Arsenal were beaten 2-1 when Dortmund visited North London last month.