Dylan Walker and Aaron Gray, who play for National Rugby League side South Sydney Rabbitohs, were prescribed the drugs following surgery last week.
Rabbitohs chief executive John Lee says both players are in a stable condition.
"They're pretty knocked around and at this stage not in a state where they can communicate, but their vital signs are very clearly on the up," he said.
Gray, 21, had an operation on his right knee, while 20-year-old Walker had surgery on his left hand.
Lee said there was no evidence of illegal drug use by either player, although NRL chief executive Dave Smith said the league's integrity unit would begin an inquiry into the incident.
Two Australian rugby league players are in hospital after they took an overdose of painkilling medication.