The music video for the song features early computer animation illustrating the lyrics. The video was one of the first uses of computer-animated human characters  and was considered ground-breaking at the time of its release.

Two other music videos are also featured within "Money for Nothing". The Hungarian pop band Első Emelet and their video "Állj, Vagy Lövök!" ("Stop or I'll Shoot!") appears as "Baby, Baby" by "First Floor" during the second verse (The name "első emelet" translates to "first floor", and the song is credited as being on "Magyar Records": "Magyar" means "Hungarian" in the Hungarian language.) The other one is fictional, "Sally" by the "Ian Pearson Band". The fictional album for the first video was listed as "Turn Left" and the second was "Hot Dogs". For the second video, the record company appears as "Rush Records", and it was filmed on Fisherman's Bastion, Budapest, Hungary.

Originally, Mark Knopfler was not at all enthusiastic about the concept of the music video. MTV, however, was insistent on it. Director Steve Barron, of Rushes Postproduction in London, was contacted by Warner Bros. to persuade Knopfler to relent. Describing the contrasting attitudes of Knopfler and MTV, he said:

The problem was that Mark Knopfler was very anti-videos. All he wanted to do was perform, and he thought that videos would destroy the purity of songwriters and performers. They said, "Can you convince him that this is the right thing to do, because we've played this song to MTV and they think it's fantastic but they won't play it if it's him standing there playing guitar. They need a concept."

Barron then flew to Budapest to convince Knopfler of their concept. Meeting together after a gig, Knopfler was reportedly still unimpressed, but this time his girlfriend was present and took a hand. According to Barron:

Luckily, his girlfriend said, "He's absolutely right. There aren't enough interesting videos on MTV, and that sounds like a brilliant idea." Mark didn't say anything but he didn't make the call to get me out of Budapest. We just went ahead and did it.

Ian Pearson and Gavin Blair created the animation, using a Bosch FGS-4000 CGI system and a Quantel Paintbox system at CAL Videographics (Peter Claridge's company in London). The animators went on to found computer animation studio Mainframe Entertainment (today Mainframe Studios), and referenced the "Money for Nothing" video in an episode of their ReBoot series. The video also includes stage footage of Dire Straits performing, with partially rotoscoped animation in bright neon colours, as seen on the cover of the compilation album of the same name.