The 70-year-old former French and U.S. Open champion is provisionally banned from all International Tennis Federation (ITF) events after hurling allegedly racist and sexist comments during Romania's Fed Cup tie with Britain last month.
All England Club chairman Philip Brook said he "condemned" the behaviour of two-time Wimbledon runner-up Nastase.
"In terms of an invitation to the Royal Box, he won't receive one this year," Brook said at the club's spring news conference.
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Club chief executive Richard Lewis went further, saying Nastase "could be stopped at the gate" if he tried to enter the grounds with a ticket.
Romanian Fed Cup captain Nastase, who courted controversy throughout his career, was booted out of his country's tie with Britain for "unsportsmanlike" behaviour.
The singles rubber between Britain's Johanna Konta and Sorana Cirstea was briefly suspended after remarks made by Nastase to Konta and Britain's captain Anne Keothavong.
Nastase had already run into trouble during the World Group II playoff tie in Constanta, after allegedly making a derogatory comment about American great Serena Williams's unborn child.
(Reporting by Martyn Herman; editing by Richard Lough)
