"Baby" was written by Keith Crouch, Kipper Jones and Rahsaan Patterson, while production was handled by the former. Conceived within a few days only, the song was created during additional songwriting sessions with Patterson, with whom Crouch had worked on several songs for the Brandy album. On the production process, Patterson commented in 2011: "I remember going over to his [Crouch's] house for two nights in a row and from the first night that he wanted to play the track for me, I heard what I heard, but I kept it to myself because I was pretty much intimidated thinking he would think it was horrible. Then by the third day, he was like “We’ve got to turn this song in by Friday, so whatever you think of, just sing it!” So I sang to him what I had heard instantly when he played it and he was like “Man you’ve been sitting there holding that!”. Most of the background vocals and instruments were recorded in one of Crouch's bedrooms. Upon hearing the demo track, Norwood applauded the song for its "flavor and soul". During recording, she was reportedly inspired by idol Whitney Houston vocally, "I wanted to be exactly like her musically!".
The accompanying music video was directed by Hype Williams and filmed in the middle of Times Square in New York City in December 1994. Choreography was handled by Fatima Robinson.[not in citation given] The video portrays Norwood and her company dancing at the "The Great White Way", wearing skiing outfits. Norwood wears a big white jacket and thin, white leggings complete with a white hat and black shades. The back up dancers are dressed in white too. The next cuts show Brandy wearing pink in a pink room & Brandy singing into a microphone in a dull coloured room. Norwood is later seen dancing with people in the same room with the rest of the video containing similar cuts. Norwood commented on filming, "all these people were passing by and were like ‘Who’s this girl on stage in the middle of Times Square?’ I had a great time shooting the video. I could just feel myself really starting to open up, really come out of my shell and find myself as a young artist."