Wicks was among a handful of leading British runners in Sunday's race aiming to win a place in the 2012 Olympic marathon team.
The Belgrave Harrier had realistic hopes of achieving the qualifying time of 2 hours 12 minutes after running 2:15:38 in Amsterdam last October and a period of training which had left him in 'great shape'.
Wicks developed the injury after running a 63-minute half marathon earlier this year and finishing third in the UK Inter Counties Cross Country championships.
"I am completely devastated that what appeared to be a minor injury has failed to respond to treatment," said Wicks.
"This has led to the very hard and agonising decision to withdraw from this year's London Marathon.
"I would like to thank David Bedford and the London Marathon for their support and hope I can return in the future to produce a performance that reflects my true abilities."
His withdrawal leaves Lee Merrien, Benedict Whitby and Andi Jones as the leading contenders to win the two remaining places on Team GB with Scott Overall, who will set the pace this Sunday, selected last year.