The US Soccer Federation announced the setbacks on Monday, two days before the Americans play host to Belgium with another match on Sunday at Washington against Germany, home nation of USA coach Jurgen Klinsmann.
Edu has a sports hernia that was diagnosed after he returned to English Premier League club Stoke City following a loan to Turkish side Bursaspor.
Houston's Ashe suffered a groin strain in a 1-1 Major League Soccer draw on Sunday against Kansas City. He had been called in only for the Belgium match.
Another USA midfielder for Stoke City, Brek Shea, dropped out with a strained right calf. He will travel to Dallas for treatment and return to the squad when he is fit but no timetable was set for his possible return.
Brazil 2014 qualifying resumes for USA on 7 June at Jamaica with the Americans returning home to Seattle on 11 June to entertain Panama and to Salt Lake City to face Honduras on 18 June.
The Americans are third on the qualifying table after three of 10 matches, with only the top three clinching berths in Brazil next year. The fourth-place team will play a two-game series against New Zealand for a trip to Brazil.