Finkler had planned to be in Brazil for the birth but Rafaela arrived early.
The 31 year old Finkler will miss Saturday's home match against Melbourne City and the fixture away to the Brisbane Roar a week later and return to New Zealand on February 27th for the Phoenix' clash against in Auckland on March 4th.
Finkler has played 18 of 19 games this season, scoring two goals and registering a lone assist.
He has come off the bench in the last two games for the eighth-placed Phoenix, both ending in 3-1 losses to Western Sydney and Sydney FC.
