Wenger, who said that everyone at the club was sending their best wishes, is confident that Rice can emerge victorious from his battle with the disease.
"It's very sad news," he told the club's official website. "Not only do we love him but of course we are very grateful for what he has done here. We are in touch with him but I trust his legendary strengths to get over that. I'm confident that he still has the fighting spirit he always had to get over that and that he will come out in a successful way.
"[His strength of character] is what he needs now - [and] he has that. In such a difficult period it's a huge resource. His mental state is very determined, very strong as he always has been. He will fight for that, I have complete trust that he will come out in a very strong way and of course let's hope for the best."
The club officially announced the news earlier on Thursday.