Kim Kardashian has been honoured by the Council of Fashion Designers of America (CFDA) and used the award to call for the industry to be inclusive of all body shapes.

Kardashian was awarded the first ever Innovation Award presented by Amazon Fashion for her shapewear brand SKIMS.

Founder and CEO Jens Grede and founding partner and chief product officer Emma Grede joined Kardashian to receive the award.

The CFDA Fashion Awards – the industry’s equivalent of the Oscars – were held in person on Monday night and hosted by actress Natasha Lyonne, and designers and CFDA members Joseph Altuzarra, Gabriela Hearst, Aurora James, Lazaro Hernandez and Jack McCollough.

The evening commemorated the history of American fashion and 60 years of the CFDA.

“We have put a strong emphasis since our launch on continuing to shape the industry to embrace size equality and diversity as a fixture and not just a trend and I see so many of you are doing just that,” Kardashian said to the audience that included her sisters Khloe and Kendall and her mother, Kris Jenner.

Martha Stewart presented the award to Kardashian, who had to make a quick announcement when a phone rang right before she started speaking. “Mom, turn your phone off,” Kardashian said to Jenner to laughter from the audience.

This year, Law Roach was honoured with a new award recognising stylists for their work.

He shared with the audience that he was watching the CFDA Awards in 2016 from behind the scenes as Zendaya’s stylist.

“I watched from the kitchen as the waiters served your food and I just said to myself, ‘One day I’m going to be on that stage.’ I am an example that anything and everything is possible,” Roach said.

Bradley Cooper, Trevor Noah and Christina Ricci were among other presenters on a night when a variety of designers took home trophies and Lenny Kravitz received the CFDA’s Fashion Icon Award.

“(Kravitz is) effortless, cool, eclectic, fearless,” Cooper said while introducing Kravitz. “Whatever it is, he’s got it. And when it comes to fashion, there’s no one cooler. There is no other musician alive today who wears leather and leopard-like Lenny.”

“My mother’s closet was my own personal boutique. I put on scarfs, belts, platform boots, boas emulating my heroes from the Jackson Five, Jimi Hendrix, Sly and the Family Stone, David Bowie and Miles Davis,” Kravitz said, recounting his youth growing up in the late 60s and 70s.

Last year, Zendaya was the youngest person to win the Icon award. Previous recipients have included Beyonce, Lady Gaga, Pharrell Williams, Rihanna and Jennifer Lopez.

Cher also made a surprise appearance to present an honour to stylist Patti Wilson. “Fashion is to be fun and feared and Patti Wilson is fearless,” Cher said.

The accessories design award went to Raul Lopez and the award for American emerging designer went to Elena Velez.

In the American designer categories, Catherine Holstein won the womenswear prize for KHAITE and Emily Adams Bode Aujla took the prize for menswear designer.

The Board of Trustee’s Award went to Virgil Abloh to honour the late designer’s contribution to global fashion. The award was received by his wife, Shannon Abloh, who said “what he was able to accomplish in his short 41 years will live on to inspire all of us for decades to come”.