Red Bull confirmed this week that the highly respected and successful Newey would be leaving the team in early 2025.
The move came after the long-running controversy around allegations over the behaviour of Red Bull team principal Christian Horner.
"I think the stuff that's going on there is a bit destabilising. It's probably the first domino to fall," Brown told a news conference at the Miami Grand Prix.
"My guess is he's not the last based on the resumes that are flying around."
Horner was accused of sexual harassment and inappropriate behaviour by a female employee.
The team principal was cleared in February of wrongdoing by an internal investigation carried out by Red Bull's parent company before the employee was then suspended. She is appealing that decision.
Brown suggested that Newey's departure may have been connected to that saga, saying he was not shocked by the technician's exit.
"Six months ago I would have been surprised. I think given everything that has gone on since the start of the year and knowing Adrian pretty well, and he's a very high integrity individual, I'm not surprised, he's moving on," he said.
"We have seen an increase in CVs coming in our way from the team and Adrian is the most successful designer of all time," added Brown.
“People want to work for people like Adrian Newey. I think they will be missing what he brings from a pure technical point of view and then the leadership and the excitement you get from working with him will be missed."
Brown did not rule out a move for Newey from McLaren but said he was "very happy" with his technical line-up.
Horner had earlier dismissed the idea that Newey's decision was a result of the tensions within the team.
"Absolutely not. This has been coming for some time," he told Sky Sports.
"There was discussion pretty much 12 months ago that it might have been the time for Adrian to look at stepping back, so I know it has been on his mind for some time. It's something we've had to plan for."
The British-based Red Bull team has won six constructors' titles and seven drivers' titles, split between Sebastian Vettel and Max Verstappen, with Newey-designed cars to date.
They are on course to do the double again in 2024, with Dutch driver Verstappen the dominant force in the sport.
Ferrari, soon to be joined by Lewis Hamilton, are reported to be in pole position to sign up Newey with the British driver saying on Thursday that he would welcome such a development.
