The British former world number one first became aware of the issue at last month's US Open.
A scan conducted after his return to the UK revealed tendonitis of the psoas: the muscle which joins the lower back to the top of the leg.
Murray stated in a social media post that he decided to pull out after some practice on Sunday.
"I've been trying to deal with it in training, and in the matches, and unfortunately after my match here this week it's flared up again," he stated.
"I've been practising the last few days and trying to manage it, but after playing some points today, I decided it was not going to be good enough to play."
Murray had been due to face the Serbian wildcard Danilo Petrovic in the first round.
Speaking before last week's opening round defeat to Fernando Verdasco, in the first of two back-to-back tournaments in Cologne, Murray stressed the importance of getting matches under his belt.
"I want to try and play matches and get tournaments in, because physically my body tends to feel better the more I play," he told reporters.
Murray may yet seek a wildcard for the Paris Masters, which starts in two weeks' time. The only ATP event arranged after that is the following week's new tournament in the Bulgarian capital Sofia.
It is almost a year to the day since Murray gained the European Open in Antwerp just nine months after hip resurfacing surgery.
His prospects seemed bright, but injuries, and the five-month Covid-19 suspension, have restricted the 33-year-old to just seven matches so far this year.
“I will see you on the court soon,” Murray signed off, without specifying how long he will be out for.
