The US president prompted confusion after using a tribute to Franklin – who died aged 76 on Thursday after suffering from pancreatic cancer – to claim the legendary soul singer worked for him on “numerous occasions”.
“Aretha Franklin passed away, I’m sure you heard, and of course this guy says, ‘Yeah, she worked for me,’” Maher said on Real Time on Friday.
“She worked for you? A complete lie. This guy cannot say ‘rest in peace’ without lying.”
After Franklin died, Mr Trump told White House reporters: “She worked for me on numerous occasions, she was terrific – Aretha Franklin – on her passing. She’s brought joy to millions of lives and her extraordinary legacy will thrive and inspire many generations to come.”
“She was given a great gift from God – her voice, and she used it well. People loved Aretha. She was a special woman.”
It was not clear what Mr Trump meant by claiming he employed Franklin, but he may have been referring to a performance by her at one of his Atlantic City casinos in the 1980s. Franklin also attended the grand opening of Trump Tower in 1997.
Franklin famously performed at Mr Obama’s inauguration in 2009, but reportedly refused to do the same for Mr Trump when his presidential campaign approached her in 2016.
The singer, known as the Queen of Soul, said “no amount of money” would convince her to perform at Mr Trump’s inauguration, according to The Daily Beast, which reported a source with knowledge of Franklin’s views as saying she “despised” the billionaire.
Maher also criticised Fox News for mistaking Franklin for Patti LaBelle.
“New rule: if Fox News is going to run, as they did, a tribute to Aretha Franklin featuring a photo of Patti LaBelle - they did that – BET must run this tribute to Barbara Bush,” Maher said, before showing a photo of Christopher Lloyd’s Doc Brown from Back to the Future.
Fox News included a photo of fellow soul singer LaBelle as part of the network’s obituary image for Franklin.
At the end of an America’s Newsroom segment memorialising the late singer-songwriter, Fox News cut to a still image of Franklin. It was captioned “Aretha Franklin, singer, 1942-2018” and featured a background photo of LaBelle singing for PBS in 2014.
“We sincerely apologise to Aretha Franklin’s family and friends,” Jessica Santostefano, a Fox News vice president, said in a statement. “Our intention was to honour the icon using a secondary image of her performing with Patti LaBelle in the full-screen graphic, but the image of Ms Franklin was obscured in that process, which we deeply regret.”