The duo, who play for Liverpool and Leeds United, have been withdrawn from selection for the clashes with Scotland and Croatia due to shoulder and calf problems respectively
Liverpool midfielder Allen had already been a doubt for selection due to an ongoing shoulder problem, as Reds boss Brendan Rodgers confirmed he will need surgery, while Leeds forward Morison is suffering from a calf injury.
The news represents a blow to Chris Coleman's hopes of improving his side's faint hopes of qualification for Brazil 2014, with both Allen and Morison key members of the Welsh squad.
23-year-old Allen had looked set to take part in the double header despite his troublesome shoulder injury. However, after being withdrawn at half time of Liverpool's 3-1 defeat at Southampton on Saturday, the decision to operate has been brought forward by the club.
In response to Morison's absence in particular, Coleman has called up Millwall striker Jermaine Easter, who is currently on loan at the New Den from Crystal Palace.
The 31-year-old, who has played 10 times for his country without finding the net, scored at the weekend on debut for his new club in a 2-0 victory at Charlton.
Wales currently lie second-bottom of Group A with only Scotland below them, the team that has provided Coleman's men with their only three points of the qualification campaign so far.