Dixon had surgery on a lingering ankle complaint and Monfries an operation on his left shoulder after a training mishap last week.
Both players are expected return to full training after Christmas.
Port’s high performance manager Darren Burgess said Dixon felt discomfort in his left ankle, a problem which caused him to miss time last season.
“Charlie has a history of ankle issues and this is the same ankle that gave him problems towards the end of last season, so we thought the most sensible thing to do is get it cleaned up now,” Burgess said in statement.
“He’ll be back running in three to four weeks.”
Monfries, who was among former and current Essenson players suspended for the 2016 season because of the Bombers’ 2012 supplements scandal, was hurt at training last week.
“The damage isn’t that bad but like Charlie, we just feel it’s safest to get the shoulder right now so there are no issues down the track,” Burgess said.
“He’ll be back running in a few weeks but will stay out of full contact drills until after Christmas.”
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