"I'm disappointed to not take to the court in Perth today," said Williams after sustaining the injury while practicing ahead of the USA's tie against Ukraine. "I had every intention to play this morning.
"Unfortunately due to inflammation in my knee, I need to rest and am confident to be out there against Aussie Gold tomorrow evening."
In November, Williams' coach Patrick Mouratoglou revealed the American star is managing a similar injury to that which has hampered Rafael Nadal in the past.
"The cartilage is not gone, not all of it, but a big part," said Mouratoglou. "She has bone bruises and if you keep on playing with this for too long, the next step is a stress fracture.
"At her age, her career could really be in danger if she went too far and got more injured like Rafa [Nadal] did in the past. He kept on playing with the same problem and then it got worse and he had to stop for almost a year.
"We don't want this to happen. She is 34. If she has to stop for a year then it is really bad for her."
During 2015, Williams was two matches away from adding another grand slam to her haul of 21 and on course to complete a calendar-year grand slam before her shock defeat by Roberta Vinci in the U.S. Open semifinals.
Williams is using the Hopman Cup -- an annual mixed team event between eight nations -- as preparation for the defense of her Australian Open crown as she aims to draw level with Steffi Graf and go second on the all-time grand slam winners list.
Tournament director Paul Kilderry said Williams initially felt pain while practicing on Sunday, but was unwilling to pull out of her match before testing her knee again on Monday.
"She wanted to give herself every chance to play," said Kilderry. "She warmed up this morning, but common sense prevailed, and she just thought today she can't do it."
Williams was replaced on the U.S. team by 20-year-old Vicky Duval who eventually lost to Elina Svitolina 6-4 6-1.
Ukraine triumphed in the tie 2-1 after Alexandr Dolgopolov beat Jack Sock 6-4 6-2, though Duval and Sock claimed victory in the mixed doubles with a 6-2 6-3 win.