The Celebrity Big Brother winner twisted his ankle after falling down a flight of stairs while rehearsing for his new theatre tour Wildboyz.
He carried on with rehearsals but later strained his hamstring during a routine, according to a statement released on his website.
"His producer accompanied him to his Harley Street Physician for an emergency MRI Scan and treatment this afternoon. Following this he broke a tooth when he banged his face on his car door so remained in Harley Street for a further two hours having cosmetic dentistry," the statement continued.
"Alex has completed a successful training programme over the last five weeks and has completed two 20 mile runs and a series of half marathons. He was running in aid of The British Heart Foundation and remains committed to the charity for next year's marathon.
"He looks [forward] to working with The British Heart Foundation on other projects as the charity is very close to his heart."
Reid added: "I'm absolutely gutted I am being forced to pull out as it's a dream I was looking forward to achieving. I was running for the BHF as my dad had a heart attack two years ago and received fantastic care.
"I know first-hand how important heart health is and I can't wait to take on the challenge of running a marathon. I am delighted I can help raise awareness of heart disease and hopefully encourage lots of support and vital funds. I have raised £2,000 so far (TBC)."
Donations can still be made via his JustGiving page.
Reid's injuries have been accommodated by Wildboyz producers, who have reworked the script.
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