Australia claimed the match 38-16 at the London Stadium, however Thaiday was forced from the field following a heavy collision with England forward James Graham.
The pair clashed heads, with the Australian coming off second best, and was taken to hospital for scans on the injury.
“Unfortunately it will probably put [Thaiday] out of the game next week,” Australian coach Mal Meninga said post-match.
“I think it was accidental.”
Kangaroos playmaker Cooper Cronk echoed those sentiments after the comprehensive victory.