Among the stores targeted for closing in its location at 610 S.E. Greenville Blvd., one of four locations in Greenville.
Mattress Firm said it expects to complete a prepackaged restructuring within 45 to 60 days.
Mattress Firm is now considered to be the US' largest specialty mattress retailer with an estimated 3,272 stores across the United States, according to Wedbush analyst Seth Basham. Stores are expected to close "in certain markets where we have too many locations in close proximity to each other", said Mattress Firm Executive Chairman, President and CEO Steve Stagner.
Online reviews have replaced going to a store to lie down on a mattress.
Two stores are less than a mile apart on Town Center Parkway.
The company said it will take steps to ensure that deliveries will be made as scheduled and without interruption.
In Southwest Virginia, Mattress Firm operates seven locations.
The retailer, which went on a buying spree in recent years adding regional chains, has secured $250 million in special financing to support operations while it reorganizes.
At the time then-Steinhoff CEO Markus Jooste - who abruptly resigned in December 2017 amid a still-ongoing accounting scandal - said the acquisition would allow Steinhoff to enter the USA market and expand its global reach.
Steinhoff bought Mattress Firm for $3.8 billion two years ago, but the chain expanded too aggressively, suffered from ineffective marketing and has been embroiled in a dispute with suppliers, Steinhoff said.
The scandal wiped more than 90 percent off Steinhoff's market value and brought the company under intense regulatory scrutiny.
"The past few years have been tough for Mattress Firm".