The guitarist reveals the accident occurred last week (ends07Mar14), and now he's hoping to make a speedy recovery so he can play through the pain and honour the concert commitments he has lined up for later this month (Mar14).
A statement issued to NME.com reads: "I was running pretty fast and just went straight over. I banged my shoulder and then realised my hand was in a bad way. Obviously we're hoping there's no long term damage.
"The plan is to do the Leeds Brudenell shows (in England) on March 24 and 25 and then the dates I have in South America, as long as I can play the guitar, when the plaster comes off.
"Usually that would be after six weeks but I'm hoping it will be Ok. It's a bit up in the air at this point."
Marr admits he has a B-plan to play through the pain on tour: "I may have to start drinking heavily."