Istvan Horvarth, who was the caretaker at the Lidl store in Hadley, won an unfair dismissal claim at Birmingham's Industrial Tribunal Court.
Mr Horvarth claimed that the tattoo was a Buddhist peace symbol.
Bosses at the store said that the angle of the tattoo resembled the Nazi symbol.
Judge Ian Miller in his reserved judgement ruled that Mr Horvarth was unfairly dismissed and should, instead, have received a warning about the company's uniform policy.
The employment tribunal was told that Mr Horvarth started worked at the Telford Hadley store as a caretaker in 2013.
In April 2019 a colleague complained that he had approached him on his second shift at the store to ask about his tattoos.
He claimed Mr Horvarth then showed him his swastika tattoo whilst laughing and saying it was his country's national symbol.
The colleague said he thought it was disgusting for someone to brazenly show it as a proud symbol.
"I come from a military background so I was not impressed for that to be displayed so publicly in a company that promotes equality and the acceptance of people from different backgrounds," he told the tribunal.
The colleague reported the incident to manager Craig Taylor who suspended Mr Horvarth after also receiving a complaint that he had kicked another colleague.
He was fired after a disciplinary hearing conducted by Lidl Area Manager Andrew Shaw.
Mr Shaw he felt that him showing the tattoo at work was damaging to Lidl's reputation.
Judge Miller agreed that the symbol was offensive and that Lidl's research into the tattoo did show that it resembled a swastika.
"Clearly it is beyond any sensible doubt that a Nazi swastika is offensive to most people for obvious reasons."
But he ruled that a stern warning about uniform policy would have been more reasonable than firing Mr Horvarth.
Upholding his claim for unfair dismissal, the judge found that Mr Horvarth was not given the opportunity to respond to all the allegations against him during the investigation and disciplinary hearing processes.
Judge Miller dismissed Mr Horvarth's claims for race discrimination were dismissed. A hearing to determine compensation will take place at a later date.