Surrey seamers Dernbach and Meaker will attend the funeral of their former team-mate Tom Maynard on Wednesday, while England bid to take an unassailable 3-0 lead over Australia. Maynard died in an incident on a London Tube track, at the age of just 23, last month. His funeral will take place in his native Wales.
It was later confirmed that, in addition to his compassionate leave, Dernbach has suffered a side strain that will rule him out for the remaining three matches of the series.
Dernbach picked up the injury during the second ODI win at the Oval and will return to Surrey for treatment.
Meaker was brought into the England squad before Sunday's victory at The Oval as cover for the injured James Anderson, who was replaced by Dernbach as Steven Finn's new-ball partner.
England are still hoping Anderson will be fit after his groin injury for the remainder of the five-match series, but have brought in Warwickshire seamer Woakes as a precaution for possible inclusion on his home ground.
All-rounder Samit Patel, yet to feature in the series, will train in Birmingham tomorrow before being released to play for Nottinghamshire Outlaws in the Friends Life t20.
He will rejoin England after that evening match.