Willett was due to tee off at 8:11 a.m. at Bay Hill, but he pulled out because of illness and was replaced in the field by American Blayne Barber.
The world No. 14 will now have just one tournament, next week's WGC-Dell Technologies Match Play in Texas, to find some form ahead of the year's first major championship.
Willett was fifth in the Maybank Championship in February after failing to convert a three-shot 54-hole lead, but then missed the cut in the Honda Classic and was 69th in a 77-man field in the WGC-Mexico Championship.
Willett, 29, tweeted: "Really sad to have to withdraw from the @APinv I've been up all night with terrible sickness. Not ideal but felt it worse to take a spot from the first reserve if I wasn't able to finish.. come Sunday im sure there'll be great champ once again."
This week's event is the first since Palmer's death last year. The seven-time major winner, who died at the age of 87 in September, started the event that bears his name in 1979 after buying Bay Hill Club and Lodge four years earlier.
A 14-foot bronze statue of Palmer was unveiled at the course on Saturday, while Willett was among the players who had the tournament's "umbrella" logo on their bags for the week.