Jones is scheduled to see a neurologist Monday.
The U.S. also will be without midfielder Graham Zusi, who drew his second yellow card against Jamaica.
Questionable is forward
Two years ago, Altidore strained the same hamstring and missed more than a month.
U.S. Coach Juergen Klinsmann could opt to be cautious with Altidore, given that Tuesday's game will be played on a temporary grass field laid over the artificial surface at
Panama is one of two unbeaten teams remaining in the six-team regional qualifier for the 2014 World Cup. The U.S., which hasn't lost since dropping its opener to Honduras in February, is second in the standings, trailing Costa Rica on goal differential.