The Republic of Ireland U21 international suffered the injury on his right leg on Thursday morning and he will begin his rehabilitation at Finch Farm in the next few weeks.
Everton U21’s boss David Unsworth said: “It was a freak accident. The boys are all gutted for Sam because they are a close group and he’s a popular member of the squad.
“We will give him all the support he needs and I look forward to having him back amongst us as soon as possible.”
Bryne joined the Toffees from Manchester United in 2014 and last month he scored in Everton U21’s win against Southampton.
Last season Bryne was named the Republic of Ireland U19 Player of Year after an impressive seven goals in only 10 appearances.
The 20-year-old is yet to make a first-team outing for the Merseyside club but he enjoyed a loan spell while on the books of Manchester United as he spent six months at Carlisle United making 13 appearances and scoring a single goal in the 2013-14 season.
Below is match highlights which include the 20-year-old strike against Southampton U21’s in their U21 Premier League Division 1 clash agile project methodologies.
Footage courtesy of Southampton FC