The 33 year-old was due to face Mackenzie McDonald in the first round of the men's singles but will now be replaced by Nuno Borges.
The news comes amid a positive run of form for the former US Open winner and Wimbledon finalist, who had recently reached the semi-finals of both the French Open and Queen's Club Championships.
Cilic, who had notably practiced with Novak Djokovic on Centre Court at the All England Club last Thursday, explained the news via a Twitter post.
"Hey guys, I am sad to share that I tested positive for COVID," he said. "I have been self-isolating and was hopeful I would be ready but unfortunately, I am still feeling unwell and unable to compete at my best.
"I am heartbroken to be missing Wimbledon & to see my grass season end this way. [I am] Looking forward to competing next year!"