FIFA agreed Friday with the Asian Football Confederation to delay next Wednesday's scheduled first-leg match by one week until 2 March.
"The joint decision was taken in order to ensure that all parties concerned can organize this match and play it in a totally safe and secure environment," FIFA said in a statement.
The match could later be switched to a neutral country.
"In the event that the situation in Yemen does not clearly improve in the next days, the match would need to take place on neutral ground," the governing body said.
Police fired tear gas on Friday at protesters in Yemen demanding the removal of President Ali Abdullah Saleh.
Yemen is due to host Singapore at the Ali Muhsen Stadium in Sanaa, in the first round of Asian qualifying for the 2012 London Games.
The return match in Singapore between their under-23 teams is scheduled for March 9.