The costume was popularised by Perry's Super Bowl halftime show earlier this year
Perry recently suggested that Swift “capitalises on the take down of women” following the singer’s criticism of Nicki Minaj and her recent single ‘Bad Blood’.
‘Bad Blood’ is rumoured to be written about Perry herself and references their tense relationship.
At the Massachusetts show, Swift was seen alongside Perry’s signature Left Shark dancer as she performed the aforementioned hit.
The Left Shark backing dancer costume was popularised by Perry’s Super Bowl halftime show earlier this year. Perry recently failed in her attempt to trademark the design.
Watch a fan-shot video of Swift with Left Shark below.
Meanwhile, Perry has hinted that she would be open to running for office in the future after meeting former US Presidents, George W Bush and Bill Clinton.
The pop star recently attended the annual So The World May Hear Gala in Minnesota, pictured at the event with the 42nd and 43rd Presidents of the United States. In a caption with the image, Perry wrote: “42, 43, 46?!”
The singer has previously expressed her intention to back Hilary Clinton to become the 45th President. Last year, she said that she would write a theme song for Clinton’s Presidential campaign.