The ads contained clips from the film, released in May, including one in which an alien egg cracks and an alien mouth suddenly shoots out of it, towards the camera.
Three people complained that the ads, seen on large screens in central London stations, would be likely to cause fear and distress.
JCDecaux, which manages the screens in question, said it believed it was appropriate to run the ads on the grounds that the scenes used also formed part of TV ads for the film.
But the ASA upheld the complaints, saying that since the film was rated 15, Twentieth Century Fox, the distributor, should have taken particular care to ensure that scenes used in the ads would be suitable to be shown in a public space where children were likely to be present.
Alien: Covenant is a sequel to 2012’s Prometheus, and a prequel to the original Alien movies starring Sigourney Weaver.