The 37-year-old rapper - who has 18-month-old daughter North with wife Kim Kardashian West - was speaking about his fashion teacher Louise Wilson, who was a professor of fashion design at Central Saint Martins College of Arts and Design in London and who died last year, when he started sobbing on BBC Radio 1.
In an interview with Zane Lowe, he said: "I went to Louise Wilson's memorial. The greatest fashion instructor of all time. And I'm talking about of all-timers, if we're talking about Paul McCartney, then we have to talk about Louise Wilson.
"Louise Wilson was the baddest professor of all time, of any fashion school, ever. Notorious, for not letting people stop at a seven or an eight, pushing people to a 12."
After praising the instructor's persistence when it came to inspiring her students, the Bound 2 rapper recalled the pair's last meeting before her death in May 2014 when she advised him on raising his daughter, which caused him to start sobbing and the interview to be halted.
He explained: "Last time I saw her we had dinner at Hakkasan which is my favourite restaurant in London and I think she knew that she was going to pass, and she just wanted to give me some words of advice.
"She was asking me about my daughter and about my wife, and she said so many students, they don't give it their all, and the problem is as soon as they do anything halfway good when they're two years old, three years old, their parents clap. And she just looked at me and said, 'Kanye, don't clap'.
"I didn't know we were going to lose her. And she told me, she said, thank you for the times when we came to performances, and this really meant a lot to me.''
However, the performer later returned and explained he was "OK" following the emotional moment.
He added: "'That's never happened to me in an interview before. I'm OK."
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