Accepting the trophy via a pre-recorded video from Britain - where he was performing - Harris instead thanked Rihanna, who performed on the track.
'I had a show tonight in the UK, or else I would definitely be there,' he said.
'Thanks, Rihanna, from the bottom of my heart. You’re a superstar.'
The award was the first of the night for Harris, whose track is also up for best collaboration.
This Is What You Came For was released in April, with Calvin and Taylor splitting the following month.
News broke in July that Swift had co-written the song.
The 26-year-old singer/songwriter previously used the pseudonym Nils Sjoberg for the song she wrote with her DJ ex.
After her involvement was revealed Taylor's name was added to the credits by BMI, which protects licenses for songwriters.
After Taylor's team confirmed that she co-wrote the song, Calvin took to Twitter to slam her for trying to 'tear [him] down'.
He wrote: 'And she sings on a little bit of it too. Amazing lyric writer and she smashed it as usual.
'Hurtful to me at this point that her and her team would go so far out of their way to try and make ME look bad at this stage though. I figure if you're happy in your new relationship you should focus on that instead of trying to tear your ex bf down for something to do.