The 72-year-old star - whose mother-in-law, Gladys Furnish, recently passed away - made the announcement via Twitter, apologising to his loyal fans in Indiana.
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Elton - whose statement did not mention the death of his mother-in-law - wrote on the micro-blogging platform: "To my dear fans in Indianapolis, It is with the heaviest heart that I'm forced to deliver the news that I am extremely unwell and therefore unable to perform at @TheFieldhouse tonight.
"I absolutely hate to let my fans down, but I owe it to you to put on the best #EltonFarewellTour show possible and unfortunately that's simply not possible.
"The date will be rearranged for March 2020, and I promise I will deliver the show you deserve. Thank you so much for your support and understanding. "Elton x (sic)"
Earlier this month, meanwhile, Elton revealed that David Furnish - his husband - entered rehab for an alcohol problem after failing to cope with the pressures of fame.
The filmmaker - who married Elton in 2014 - struggled to come to terms with the interest in his life, and entered himself into a rehab clinic in California around the time they tied the knot.
Writing in his new autobiography, 'Me', Elton shared: "I always thought David had slipped into Elton John World with remarkable ease and confidence, but it turned out that a lot of things I was completely used to living with, that I just saw as a fact of life, made him completely anxious.
"He didn't like being photographed all the time, or being under press scrutiny, or public speaking at [Elton John] AIDS Foundation events."
