The woman was being treated for hyperthermia at Royal Victoria Hospital, The Irish Times reported. Police said she was in the water for about 15 minutes before being rescued.
The Stena Line ferry was approaching the dock in Belfast late Wednesday afternoon after its voyage from Cairnryan, Scotland, when the two were spotted falling from the vessel in Belfast Lough.
The Irish Coast Guard, which supplied a helicopter for the search, said it had been told the baby was 9 days old.
Several Coast Guard teams, a Police Service of Northern Ireland helicopter, tugboats and a pilot boat searched the lough without result. The ferry terminal was closed Wednesday evening.
"We have been searching for the second missing person for over 2 hours but sadly we have not found any sign of them so far," Ian Murdoch, the watch manager for the Belfast Coast Guard, said at about 9 p.m.