The loss of Faletau and Biggar is a major problem for coach Wayne Pivac.
Faletau is in career-best form and a contender for player of the tournament after starring in the Welsh Six Nations triumph.
Kiwi Gareth Anscombe is near the end of a long recovery from a knee injury and could replace Biggar at No. 10. Biggar started all of the Six Nations games, with Sheedy coming off the bench.
Pivac could turn to the old combo of Leigh Halfpenny at fullback, with Liam Williams shifting to wing, to deal with the absence of Rees-Zammit.
Wales Online reported: "The head coach does have potential replacements who could plug the gaps, but let no-one pretend it's an ideal situation."