Shander, who has been with the company for four years, was not paid a US$4 million retainer that the company had negotiated with him before it was acquired by IBM, the Raleigh News and Observer reported.
A former vice-president and chief accountant at Lenovo, Shander led the formation of the global chief financial officer function at the Chinese firm after it bought IBM's PC business in 2005.
Before that he was at IBM for nearly 15 years. He rejoined IBM in 2008 before moving to Red Hat.
The page on Red Hat's website that formerly contained details about Eric Shander.
IBM completed its acquisition of Red Hat in July and the agreement with Shander was that he would get the US$4 million payout in two tranches, six months and a year after finalisation of the merger.
Red Hat has made no public statement about the firing and has removed a page on the company's website that formerly hosted Shander's profile.
IBM is due to report quarterly earnings on Wednesday US time.