Long-time boss Menezes, who was set to retire at the end of this month, is in hospital receiving treatment for conditions including a stomach ulcer, the company said in a statement.
"Over the weekend, we learned that Ivan's recovery suffered a significant setback due to complications, which followed emergency surgery on the ulcer," Diageo said.
Diageo, the maker of Johnnie Walker whisky, Tanqueray gin and Don Julio tequila, appointed Crew in March to replace Menezes, making the 52 year-old one of only a handful of women to lead a company in Britain's blue-chip FTSE 100 index.
Crew will join the board as an executive director on July 1, Diageo said on Monday.
The former U.S. military intelligence officer, who was appointed operating chief last year, had been president of Diageo North America, its largest market, and Global Supply from 2020.
She takes on the top role as Diageo is trying to cement its dominance in the United States and establish several premium brands, in a post-COVID world.
Shares in the London-listed firm are down about 7% this year.
Menezes, who joined Diageo after its formation through the merger of Guinness and Grand Metropolitan in 1997, grew sales sharply and steered the company through multiple brand acquisitions as well as a major sustainability overhaul.
"Out of respect for Ivan and his family's privacy, we will not be commenting further at this time," Diageo said.
