Ali, a native of Louisville and a former three-times world heavyweight champion, was taken out in a golf cart to greet the Europeans on the first fairway on the last day of official practice.
The 66-year-old, who has long battled Parkinson's disease, posed for photographs with the entire team before each player sat next to him in the golf cart for individual snapshots.
"That's one of those Ryder Cup moments you can't put into words," Faldo said.
Europe will be bidding for a fourth successive victory over the United States when the 37th Ryder Cup starts on Friday with the opening foursomes matches.