She was scheduled to guide the prince around an exhibit staged by The HALO Trust, of which Prince Harry is a patron, in the Russell Senate Office building.
"My wife is not able to be here, unfortunately. She had a medical problem with her knee," McCain said Wednesday afternoon.
"It's been giving her problems," McCain said. "Otherwise she would be here and is very disappointed that she's not."
Prince Harry begins a week-long trip to the United States on Thursday, where he'll be raising money for charity, visiting with veterans and touring the damage from Superstorm Sandy.
The prince was in McCain's home state of Arizona in November 2011 for military training but the senator said they did not meet at the time. He did say he would meet Prince Harry on Thursday evening at a reception at the British Embassy in Washington.
Prince Harry will be in the nation's capital for two days. On Friday he will lay a wreath at Section 60 in Arlington National Cemetery and at the Tomb of the Unknown Soldier. He will then visit with wounded service members at Walter Reed National Military Medical Center.
No meeting with President Obama has been announced.
The prince then heads to Colorado, where he will attend several events at the 2013 Warrior Games.
He'll be back on the East Coast on Tuesday, where he will tour some of the residential areas still devastated from Sandy. He'll be escorted by Gov. Chris Christie (R-N.J.).
On his last visit to the States, in August, Prince Harry made headlines for nude photos taken in Las Vegas.
Christie said that won't happen again.
“Believe me, nobody’s going to get naked if I’m spending the entire day with Prince Harry,” Christie said in a radio interview in March, when the visit was announced.
The prince will then be in New York City for fundraising events and to meet with British business leaders.
On Wednesday, May 15, Prince Harry will hold the final event of his trip: he'll play in a polo match in Greenwich, Conn. The proceeds will benefit his Sentebale charity that helps children in Lesotho, Africa.