The French centre-back suffered the injury during the second half of Wednesday's pre-season friendly against Villarreal.
Fofana was the victim of a late tackle by forward Nino and had lengthy treatment on the King Power Stadium pitch, including being given oxygen, before being carried off.
"Hello guys, many thanks for all your messages. It is a bad day today but I am in a tremendous club with a wonderful medical team," he wrote on Instagram.
"I will give you news as soon as I have a final diagnosis but we already know that I have a fibula fracture. I will come soon and stronger: do not worry."
Fofana excelled for the Foxes last season after he joined from Saint-Etienne in October for around £30million.
He made 38 appearances as Leicester finished fifth in the Premier League and won the FA Cup for the first time in their history.
Fofana's injury is a massive injury blow to boss Brendan Rodgers ahead of Saturday's Community Shield with Manchester City at Wembley.