The broadcaster published a one-to-one video with the 23-year-old who gave his answers to the questions in Spanish, with English subtitles added.
According to the translated answers, Morelos claimed he had been the victim of racial abuse from Celtic fans, which was incorrect.
Asked by the interviewer, "How often do you experience racist abuse from a crowd?" Morelos replied: "Yes, I feel there are lots of racist gestures aimed at me. At Aberdeen, for instance, they insulted my mother, me, they threw coins at me. People often throw things at me when I score at away games."
Sky Sports' original translation suggested that Morelos was accusing Celtic supporters.
The Parkhead side lodged a complaint in response to the interview and the clip was removed from their television channel, website and mobile app.
In a lengthy statement, a spokesperson for the club said: "Translations provided to Celtic Football Club have shown inconsistencies between the words spoken during the interview broadcast and the subtitles used by Sky Sports.
"Celtic FC has asked Sky Sports to clarify their position on this matter."
The broadcaster has now apologised to the player and the two clubs but The Sun reports that an Ofcom probe could be launched after 29 complaints were received relating to the interview.
A statement published on the Sky Sports website read: "We have identified inaccuracies in the translation of Sky Sports News' interview with Alfredo Morelos. We apologise to both Celtic and Rangers football clubs as well as Alfredo Morelos for the issues caused by these errors.
"After numerous steps undertaken by Sky to verify the interview thoroughly we can be clear that at no point did Morelos allege that any racial abuse was directed at him by Celtic supporters in the interview. We apologise to the supporters of Celtic Football Club for this serious error.
"We are reviewing our procedures for translated interviews to ensure this does not occur in future."