Newcastle striker Murphy, who headed the late equaliser in last month's 2-2 draw in Serbia, has a calf injury.
Stephen Quinn (knee), keeper Keiren Westwood (thigh), Kevin Doyle (ankle), Aiden McGeady (hamstring) and Anthony Pilkington (quad muscle) are also out.
Bournemouth's Marc Wilson has pulled out because of a lack of recent action.
Like Murphy, Reading midfielder Quinn made a positive contribution when introduced off the bench in Belgrade.
The other players ruled out are also not regular starters, but the volume of injuries reduces Martin O'Neill's options for Thursday's home game against Georgia and Sunday's match in Moldova.
In addition to the seven withdrawals, O'Neill has fitness concerns over Everton midfielder James McCarthy and Bournemouth's Harry Arter, who both have groin injuries, while Leeds midfielder Eunan O'Kane is also nursing a knock.
With Sheffield Wednesday's Westwood ruled out, Manchester City keeper Ian Lawlor has been promoted from the under-21 squad, while Aberdeen striker Adam Rooney has also been called up.
The Republic boss was in philosophical mood when asked about the injuries.
"These things happen. It's part of the game. You just have to curse your luck and get on with it," said O'Neill.
"We've got a few injuries. If Adam Rooney gets a chance, it is up to him to go and take it."
Moldova were beaten 4-0 by Wales in Cardiff in their opening qualifier last month while Georgia lost 2-1 at home to Austria in their first game in Group D.
Daryl Murphy is among seven players who will miss the Republic of Ireland's World Cup qualifiers against Georgia and Moldova later this week.