The 23-year-old is to undergo treatment for the illness, which will include surgery at the beginning of next week.
A statement on Cheltenham's website said that Richards is expected to make a full recovery.
"The club will, of course, ensure that every assistance is offered to Eliot and his family to help them through this difficult time," the statement read.
"In due course, we expect Eliot to make a full recovery.
"In the meantime we know that all Cheltenham supporters will want to join us in wishing Eliot and his family well in the days and weeks ahead."
Earlier this month Newcastle United winger Jonas Gutierrez returned to action after almost a year out with testicular cancer.
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