The teaser, released Wednesday during the CMT Music Awards, features Swift with red hair starting an affair with Routh who appears to be married to Sugarland's Jennifer Nettles.
Nettles is seen enjoying a martini alone at an empty dinner table. Nettles' Sugarland partner Kristian Bush also briefly appears in the video.
"Babe," which was co-written by Swift and Train's Pat Monahan, and features vocals from the singer, is the second single from Sugarland's upcoming Bigger album, their first project since 2010's The Incredible Machine.
The music video for "Babe" is set for release on Friday.
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