The 25-year-old, who plays Mercedes Jones in the Fox musical comedy, said that she "almost started crying" when she went up to the 'I Will Always Love You' singer at Kelly Price's pre-Grammy Awards party in LA on Thursday (February 9).
"Whitney's music meant so very much to me," she told E!. "I was very very choked-up when I heard about her passing. I'd grown up listening to her voice ringing out throughout our household. I'm so speechless, I can't believe that she passed."
She added: "I didn't need her to take a picture with me. I didn't need an autograph. The fact that she even acknowledged that I was standing there was enough for me."
Asked to comment on reports about Houston's "erratic" behaviour leading up to her death on Saturday (February 11), Riley replied: "She was very, very sweet to me and I can only see her as the beautiful person that I watch on television.
"She was very sweet to me and I'm glad that's the memory I'm going to hold for the rest of my life."
Riley also said that she hasn't "been told anything" about whether Tuesday's edition of Glee, in which she covers 'I Will Always Love You', will become a tribute to Houston.
Listen to Amber Riley cover Whitney Houston's 'I Will Always Love You' for Glee below:
View Whitney's life in pictures below: