The Supreme Court judge couldn't hear the snoring but was made aware of the issue.
The judge said the woman had fallen asleep on at least four separate occasions during evidence in which police investigators were cross-examined.
"The juror's inability to remain awake ... caused me to conclude that there is a reason affecting the juror's ability to perform the functions of a juror," Hamill said.
After being told she was being dismissed, she revealed she had a medical problem which gives her drowsiness.
"It should be recorded, without reference to private information, that the juror was diligent and attentive until the last week or so of the trial, and their inability to remain awake was understandable and beyond their control," Hamill said.
The hitman, Ying Cheng Luo, and his associates Jaiyu Liu and Ian Fan, were all found guilty of murdering Chinese national Qin Wu.
They face sentencing on March 19.