A club spokesman confirmed to OMNISPORT that the 30-year-old has not travelled with the team and will continue his own preparations back in England with the club's Under-21 side.
The winger, who joined Stoke permanently in 2011 following a previous loan spell, was unable to obtain the necessary permission to head to America following a previous criminal conviction for admitting driving home drunk from a nightclub.
It is the second successive year that Pennant has been denied entry to the US and comes after Stoke manager Mark Hughes decided to show faith in him by offering him a new one-year deal, having slipped down the pecking order under Tony Pulis.
The rest of Stoke squad are preparing for matches against Houston Dynamo, FC Dallas and Philadelphia Union in America.
Stoke finish their pre-season schedule away at Wrexham on August 4 before hosting Serie A outfit Genoa at the Britannia Stadium, games that Pennant will be hopeful of featuring in.