The UK title, which launched in September 2006, employs 24 people. The last issue of the magazine was distributed on 3 April.
The company said that it had decided to suspend publication while "the company rethinks its business model".
Greg Miall, the magazine's managing director, said: "Although the magazine is tremendously popular with readers, especially the AB demographic, over the past few months we have seen several clients close down and others cut advertising spend dramatically."
Sport has an audited weekly circulation of 317,257 and is distributed to London's commuters at tube stations, gyms, health clubs and airports.
In 2008, Miall was promoted from publishing director to the magazine's managing director replacing the woman who was credited with launching the title, Nadia Nardonnet.
Hannah Murphy, head of print at Vizeum, said the title's sole dependence on advertising revenue meant it was "not a huge surprise" operations have been suspended.
She noted that it comes ahead of a potentially lucrative summer of sport for the magazine, including the Ashes being held in the UK.
She added: "No one wants to see a magazine close, especially one which has been as valued and ground-breaking as Sport."
The magazine's coverage since its inception has featured interviews with a number of sporting stars including Tiger Woods, David Beckham, Ronaldo and Rafa Nadal.
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