Draper, with new coach Andy Murray, were expected to make their return at the London tournament, but their new partnership has been delayed.
In a statement given to Sky Sports, Draper said: "[My] Recovery is going in the right direction, but I'm going to give myself one more week and aim to return at Eastbourne. Very hard to miss one of my favourite events of the year."
Draper has previously flourished at Queen's, having reached the semi-finals in 2025 and the quarter-finals in 2024, but there is a silver lining for the British star.
He will now make his return to the Eastbourne Open, where he holds similarly fond memories.
The British star has only played the event once, but that involved a brilliant run to the semi-finals of the grass court event.
Draper entered the 2022 event as a wildcard, but that didn't stop him knocking out some very big names en route to the final four of the competition.
The star toppled Jenson Brooksby, Diego Schwartzman, and Ryan Peniston to reach the first ATP Tour semi-final of his career on the South Coast.
He was eventually beaten by Maxime Cressy, but Eastbourne marked one of Draper's breakout tournaments on the ATP Tour, which could be a good sign for this year's event.
He followed that up by picking up his very first main draw victory at Wimbledon by defeating wildcard Zizou Bergs in his opening round match.
That run gave Draper the confidence to truly stamp his mark on tennis for the rest of 2022. He would go on to make his first Masters quarter-final mere months later at the Canadian Open.
The British star also claimed his first two top 10 victories of his career, against Stefanos Tsitsipas in Montreal and Felix Auger-Aliassime at the US Open.
He finished the year making his NextGen Finals debut, defeating top seed Lorenzo Musetti, and reaching the semi-finals of the competition.
If Draper can use the Eastbourne Open in a similar way this year, he could be set for a very good second half of the season and truly put his injury woes behind him.
Draper's grass court season now looks to be limited to just Eastbourne and Wimbledon, but there is every chance he can still flourish under the tutelage of Murray.
To date, the likes of Taylor Fritz, Arthur Rinderknech, Francisco Cerundolo, Tomas Martin Etcheverry, and Rafael Jodar have signed up to Eastbourne, so Draper will absolutely return to competitive action.