The US Soccer Federation announced the setbacks on Monday, two days before the US plays host to Belgium with another match this weekend at Washington against Germany, the homeland team of US coach Jurgen Klinsmann.
Edu has a sports hernia that was diagnosed after he returned to English Premier League club Stoke City after a loan to Turkish side Buraspor.
Houston's Ashe suffered a groin strain in a 1-1 Major League Soccer draw against Kansas City last weekend. He had been called in only for the Belgium match.
Another US midfielder for Stoke, 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.
North American World Cup qualifying resumes for the US side on 7 June at Jamaica with the US returning home to Seattle on 11 June to entertain Panama and to Salt Lake City to face Honduras on 18 June.
The US is 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.