The Briton had been due originally to test the 2017 Pirelli tyres with a modified 2015 'mule' car on Wednesday but team mate and championship leader Nico Rosberg took on those duties instead.
A team spokesman said German reserve driver Pascal Wehrlein, who races for Manor, would stand in for Hamilton on Thursday.
"Lewis had some discomfort in his foot after training on Tuesday," he said. "It was agreed he wouldn't test so he could rest it and get physio to be in good shape for Austin, which he will be. No concerns on that front."
Hamilton is 33 points behind Rosberg in the world championship with four races remaining, meaning that even if he wins every one it will still not be enough if Rosberg finishes second each time.
The Briton won his third title, and second with Mercedes, at Austin's Circuit of the Americas last year when Rosberg started on pole but made a mistake that gifted his team mate the victory.
Rosberg, who is now heading for his first title, then went on to win the three races after that in Mexico, Brazil and Abu Dhabi before starting the new season with four successive victories.
Both Hamilton and Rosberg were at the team's Brackley headquarters and Brixworth high performance engine facility on Tuesday, with the Briton seen to be limping slightly later in the afternoon.
Hamilton triggered a media spat at the last race in Japan when he was criticised for playing around with Snapchat during a news conference, taking pictures of fellow drivers and complaining of the boring format of the event.
He then walked out of a media briefing on Saturday and hurriedly left the circuit after the race, flying back to Europe with non-executive chairman Niki Lauda and Mercedes motorsport head Toto Wolff.
The team said then that Hamilton had to be back in Europe as soon as possible to be ready for Wednesday testing.
(Editing by John O'Brien)
