Wilson was expected to promote his new film, "The Darjeeling Limited," at the Venice Film Festival but he bowed out of all his appearances amid reports he was hospitalized after attempting to take his own life.
"When he's ready, he's going to speak for himself much better than anyone else could," Anderson said in Venice Sunday. "He has a very good way with words."
Wilson returned home this weekend and is said to be under the close watch of family and friends, People.com reported.
Anderson directed Wilson in "The Darjeeling Limited," as well as "The Life Aquatic with Steve Zissou," "The Royal Tenenbaums" and "Bottle Rocket."
"I just want you to know how excited I am to have the film showing here," Anderson said at a news conference. "It means a great deal to me and it also means a great deal to Owen. ... We all miss having him here very much. Obviously, he's been through a lot this week but he's doing well and he's been making us laugh a lot."