Former Scotland international full-back Malpas only took over at the County Ground in January following Paul Sturrock's return to Plymouth Argyle.
But he has struggled for results, with the final straw being the club's departure from the FA Cup and Johnstone's Paint Trophy to Blue Square Premier side Histon and League One rivals Brighton respectively in the past week.
The Swindon board placed a high importance on progression in the cup competitions, and the team's early exit from all of them is likely to cause a few financial headaches at the County Ground.
It leaves Swindon searching for their sixth full-time manager in just over three years, with Iffy Onuora, Dennis Wise, Sturrock and Malpas all having spells in charge since Andy King left the club in September 2005.
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