Guests at a cancer fundraiser at the mogul’s private Florida club Mar-a-Lago had paid up to £120,000 for a table to see the singer perform at the weekend.
But she pulled out of the gig at the last minute after her doctor apparently forbid her to fly from Los Angeles to Palm Beach because of acute bronchitis.
It gave organisers just hours to find a replacement - Dreamgirls star Jennifer Hudson.
And to add insult to injury, Rihanna could be seen on national television the following night singing in the half-time show for the high profile NBA All-Star game in LA.
She then tweeted to her fans at 3am the following morning saying she was partying for her 23rd birthday, according to reports.
Now no-nonsense billionaire Trump has hit back, telling the Palm Beach Post Rihanna's attitude was “insulting to everyone”.
He added: “But for Rihanna to go to the All-Star game and perform when she told us she was sick, that is just a lack of respect.
“But, nothing was missed. Jennifer’s a beautiful girl. She came on her day off even though she performs almost every night. She is an unbelievable talent, and her voice is better.”