The Tottenham Hotspur player sustained the injury in a collision with Chelsea striker Liam Delap and had to wear a mask in their final match of the season against Everton.
"It's a little bit uncomfortable but it is what it is," Spence told reporters on Monday.
"I've got a broken jaw so I have to wear it throughout the tournament. It's something I will have to get used to. It'll be three months until it's fully healed, so it's a long time."
Spence, who played to the end of the match against Chelsea, said he had not been worried that he might be sidelined due to the injury.
"It was painful but luckily I play football with my feet and not my jaw. So I was all good," the 25-year-old added.
England open their World Cup campaign against Croatia in Dallas on June 17 before taking on Ghana and Panama.