The United States international sustained the break to the bone in his ankle in training on Wednesday, with scans indicating the fracture.
“We are all disappointed that Danny has suffered this injury and now we offer him our full support as he begins his recovery,” Huddersfield manager David Wagner told media.
“He’s adapted well to football in the Premier League and has been in some great form for us recently.
“He’s a big character in the dressing room too and I have no doubt that he will be determined to come back fitter and stronger than before.
“In his absence, we will do everything we can to make sure Danny is back playing Premier League football with Huddersfield Town next season.”
The club added Wagner will have further updates on Williams’ condition on Friday.
Williams signed with Huddersfield on a free from Reading last season, after the former beat the latter on penalties in the Premier League promotion playoff final. The 29-year-old defensive midfielder played in 24 games in all competitions with the Terriers this season, making 11 starts in the Premier League. His one goal came in the FA Cup against Bolton.
Earlier this month, Williams had spoken about his desire to carve out a place for himself with the U.S. national team after being frozen out during the nation's failed World Cup qualification. Williams had captained the side in a friendly against Portugal in November and said he was looking forward to receiving a chance to feature again against Paraguay in March’s friendly.
However, this injury knocks Williams out of contention for that squad.
Meanwhile, Huddersfield remains in a battle to stay in the Premier League. The club sits in 15th, four points above the relegation zone.