The Three Lions boss was making the most of a day off from training when he sustained the injury, which left him in a local hospital.
Football Association team doctor Rob Chakraverty attended to oversee the treatment and Southgate returned to camp in good spirits but sporting a black sling.
Southgate took his tumble light-heartedly, joking he may not be allowed to show the same kind of emotion on the touchline which accompanied Harry Kane’s stoppage-time winner against Tunisia.
“I might not be celebrating any goals as athletically in the future,” he said.
“The doc has made it clear that punching the air is not an option.
“I am just a bit gutted because I was on for my record 10k time!”
Southgate’s unexpected injury news caused no great disruption to team plans – with a scheduled meeting taking place on time in the evening as preparations for Sunday’s clash with Panama continue.
“We are lucky we have a top-class medical team around us, so it was fine,” Southgate said.
“I had brilliant help from them, and I am just sorry that I managed to ruin their day off.”
Southgate joins Dele Alli on England’s walking wounded list, with the Tottenham forward suffering from a quad complaint.
While Alli’s fitness is a cause for concern, Southgate confessed his own travails were more a source of amusement among the group.
“It is better this is me than one of the players,” he said.
“They were a bit surprised in the team meeting and were asking ‘what have you been doing!?’ - as always, they were probably quite amused.”
Marcus Rashford says the England squad are relishing this opportunity to show people how far they have come, saying they are “really is a team” compared to Euro 2016.
Kane’s late heroics in Volgograd saw the Three Lions start the World Cup with a victory for the first time since 2006.
The spirit, patience and camaraderie displayed in the 2-1 defeat of Tunisia was a far cry from their last match at a major tournament, when toothless England suffered one of their most humiliating defeats.
Rashford came on for the dying embers of that galling Euro 2016 exit to Iceland, but the forward believes the group has taken huge strides since then and have kinship perhaps lacking back then.
“I think the mood around the camp is a lot calmer from what I can remember of that last tournament,” he said, comparing this squad to his first major tournament experience with England.
“But I think that’s as expected. We were all fairly new to each other in that tournament and now we’ve managed to build relationships and the team really is a team now.
“I think that only puts us in good stead for this tournament and future tournaments.”
Rashford hopes to prove himself worthy of starting England’s penultimate Group G match against minnows and World Cup debutants Panama on Sunday. “We have to show respect but get the three points.”