The 31-year-old only returned to action last week after almost a year out with the right hip problem that required surgery in Australia in January.
He has played three matches since, losing to Nick Kyrgios at Queen's Club and fellow Briton Kyle Edmund this week at Eastbourne having taken a wildcard to test his fitness.
Murray, winner of Wimbledon in 2013 and 2016, has said he would only play at next week's championships if he was certain he could be competitive and face five-set matches.
The Scot is unseeded having slipped to 156th in the rankings and his first test will be against France's Benoit Paire.
Paire was Murray's last match victory at Wimbledon, with Murray beating him in the fourth round last year before losing to Sam Querrey in the quarter-finals.
Murray did not play again in 2017 after his Wimbledon exit, pulling out of the U.S. Open at the last minute, and he eventually opted for surgery in January.
Murray is expected to practise at Wimbledon on Friday as he assesses his fitness.
(This version of the story corrects paragraph three to show Paire was last opponent Murray deafeted at Wimbledon, not last opponent).
(Reporting by Martyn Herman; Editing by Alison Williams)
