The US went on to lose 1-0 but Reyna, 1 of only 2 City players at the World Cup (David James is the other), was relieved to hear that an MRI scan showed no muscle damage.
Although no date has been set for his return, he is expected to be fit for his country's opening game against the Czech Republic on June 12.
"I am relieved that there is no serious damage," said Reyna. "I'll be working
with the trainers on a daily basis and will be focused on getting back on the
field as quickly as possible.''
Dunne, meanwhile, played 90 minutes of the Republic of Ireland's friendly with Chile at Lansdowne Road.
It was a tired performance from the Irish in Steve Staunton's second game in charge and Dunne was involved as Chile scored the game's only goal in the 49th minute.
Dunne was unable to hack the ball clear from the area after a free-kick had been blocked and Manuel Iturra managed to force the ball home.
With Ireland not making the World Cup, City's two-time Player of the Year can now take a well-earned break over the summer.