In a ceremony held at Monaco's Grimaldi Forum, the pair were honoured with the world governing body's top awards.
Kipchoge won the award for a second year running as he was honoured for being the first person to run a marathon in under two hours.
The Olympic marathon champion told the awards ceremony about his incredible achievement: "I hope I inspired the human race."
Muhammad, the Rio 2016 400m hurdles champion, broke the world record in her event twice this year in addition to winning the world title in Doha, lowering the mark to 52.16 seconds.
She was also part of the United States' winning women's 4×400m relay team.
"It's been an amazing year," she said. "It's been a tough year but I'm so thankful. I never imagined ending the year like this."
Rising stars, top coaches, and fair play recognised
Among the other award winners of the night were Selemon Barega, Yaroslava Mahuchikh, Braima Suncar Dabó, Brother Colm O'Connell, and Derartu Tulu.
Barega, the world 5000m silver medallist from Ethiopia, was named Male Rising Star of the Year for the best under-20 athlete. In addition to his silver medal from Doha, Barega also finished fifth in the World Cross Country Championships in Aarhus, Denmark, and recorded under-20 world-lead times in both the 5000m and 10,000m.
European U20 high jump champion Mahuchikh, the Female Rising Star of the Year, broke the world u20 record in Doha by clearing 2.04 metres. That height was the same as eventual winner Mariya Lasitskene, who only won on count-back.
Guinea-Bissau's Dabó was named by the International Fair Play Committee as the winner of the Fair Play Award for his selfless act in helping Aruba's Jonathan Busby complete the men's 5000m heat in Doha.
Busby, who was struggling with dehydration and the heat, was on the verge of collapsing when Dabó, the last runner in the race, stopped to support the Aruban all the way to the finish line.
Irishman Brother O'Connell, who has trained Kenya's top champions over four decades including David Rudisha, received the Coaching Achievement Award from his former protege, Wilson Kipketer (who represented Denmark). "I never intended on having a career in coaching when I landed in the Rift Valley 43 years ago," he told the awards ceremony.
Ethiopia's Derartu Tulu, the 10,000m Olympic champion at Barcelona 1992 and Sydney 2000 and the first black African woman to become an Olympic champion, was awarded the Woman of the Year Award for her contribution to the sport on and off the track, including her work as acting president of the Ethiopian Athletics Federation.
The late British athletics journalist, Vikki Orvice, was awarded the World Athletics President's Award for her work in a male-dominated industry.
"I have chosen a trailblazer in not just our sport but all sport," Sebastian Coe said. "She was a game-changer in journalism.
"She loved athletics, she loved her life and she wanted to make the most of every minute."