Tualima made his club SRP debut in the match last month, with the Brumbies becoming the first Australian team to win in Fiji.
But the 27-year-old from Queensland fell ill after the trip and was unable to play their round two match against the Western Force in Canberra.
The Brumbies issued a statement on Monday saying that testing had revealed the mosquito-borne disease.
"The team took all preventative measures against mosquito-borne illnesses, however one of our players, Tuaina Taii Tualima, has become ill after catching dengue fever.
"The affected player has been diagnosed early and is receiving medical input from the team doctor and an infectious disease specialist."
The club didn't provide a timeline for his return.
Tualima, who can also play lock, joined the Brumbies from the defunct Melbourne Rebels.
The Brumbies are currently in New Zealand following their 49-34 loss to the table-topping Chiefs, which came after their shock loss at home to the Force.
They next face defending champions the Blues in Auckland on Friday night and are already without Wallabies loose forwards Rob Valetini and Tom Hooper.
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