The advert featured the cast of The Secret Life of Pets, with one dog becoming frustrated with its broadband connectivity.
Virgin Media challenged a claim in the ad that Sky broadband was "super reliable".
The ASA drew on data from Ofcom to uphold the complaint.
It concluded that the ad could "mislead consumers" because it implied that all of Sky's broadband packages were super-reliable.
"That is not the case for Sky's ADSL2+ package," the ASA said in its summing up.
A similar Sky ad, featuring Lego Batman, was banned for misleadingly claiming to offer the UK's lowest-priced fibre.
Complaining about one another's adverts seems to have become standard practice in the internet service provider world.
In 2016, Virgin Media had a broadband ad featuring Usain Bolt banned over misleading claims about broadband speeds after BT and Sky complained to the ASA.
And a BT advert fronted by actor Ryan Reynolds was banned after Virgin complained that it implied BT's 52Mbps service was the fastest maximum speed service for the lowest-priced package in the UK.
A spokesman for the ASA said the organisation attempted to dissuade the telecoms industry from "tit for tat complaints" by asking them to provide evidence that they had approached their competitor and tried to resolve the matter between themselves first.
"It is a ferociously competitive sector and a lot of scrutiny is given to competitors' advertising, but we only act when there is a problem under the rules," he told the BBC.
Sky has had another TV broadband advert banned by the Advertising Standards Authority (ASA) following a complaint from rival Virgin Media.