Irving, has been staunch against getting vaccinated, despite a New York City order requiring the shot if he is to play or practice with the team at home this season.
"Given the evolving nature of the situation and after thorough deliberation, we have decided Kyrie Irving will not play or practice with the team until he is eligible to be a full participant," Marks said.
"Kyrie has made a personal choice, and we respect his individual right to choose. Currently the choice restricts his ability to be a full-time member of the team, and we will not permit any member of our team to participate with part-time availability.
"It is imperative that we continue to build chemistry as a team and remain true to our long-established values of togetherness and sacrifice. Our championship goals for the season have not changed, and to achieve these goals each member of our organization must pull in the same direction. We are excited for the start of the season and look forward to a successful campaign that will make the borough of Brooklyn proud."
The New York mandate prohibits unvaccinated individuals from working in or attending events at many indoor spaces, including entertainment and sporting venues. Similar rules are in place in San Francisco and will go into effect in Los Angeles as of Nov. 29.
Irving's stance potentially could cost him millions, although the players' association could move to challenge salary withholdings over vaccination status.
Marks said Tuesday that Irving would not be paid for home games he misses while "ineligible." The NBA isn't forcing players to get vaccinated against COVID-19, but it is going to withhold pay for any player who misses games due to local regulations.
Irving is due $50 million this season in the third year of a four-year, $197 million deal he signed July 6, 2019.