The professional baseball team had the memento signed by the pair in happier times when Humphries threw out the first pitch at a Twins game in July 2011.
The Twins have now officially opened a public sale on the signed baseball, where fans will be able to bid for the prize through Valentine's Day (February 14).
Proceeds from the auction will benefit the Minnesota Twins Community Fund.
Twins director of public affairs Kevin Smith said of the auction: "We have as far as we know, a one-of-a-kind item – a baseball with both of their signatures which we believe is best used to raise incremental funds for the good works of the Community Fund."
Kardashian filed for divorce from Humphries on October 31, only 72 days after they tied the knot in a lavish Montecito, CA wedding.
This week, Humphries struck back at claims that his marriage to Kardashian was a sham by insisting that his love for the reality star was always "real".
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