Jackson told The Detroit News that the singer is "recovering" and in high spirits. He did not say what Franklin, 68, is ailing from.
"She's doing very well. She's very prayerful. She's a woman full of deep religious faith," he added.
Although her rep has not revealed what kind of surgery Franklin had, the procedure has been described as "highly successful.
"I had superb doctors and nurses whom were blessed by all the prayers of the city and the country," the singer said on Thursday.