Recent speculation has linked Shawcross, 29, with a £10m move to Burnley before the August deadline passes.
Hughes, however, has insisted that the centre-back, who is closing in on 400 appearances for Stoke following a 2008 move from Manchester United, will not be leaving the Potters before the end of the month.
"You might read it but it won't happen," Hughes told reporters.
Stoke opened their 2017-18 Premier League campaign with a 1-0 defeat at Everton last weekend. On Saturday, Hughes's side will look to put their first points on the board when they host Arsenal.