The 28-year-old picked up the injury during Arsenal's 1-0 win over West Ham on Sunday and was substituted in the first half before later being seen leaving the London Stadium wearing a knee brace.
In a statement, Arsenal said: "Further to Sunday's match at West Ham United, subsequent assessments and specialist reviews have confirmed that Ben White has sustained a significant medial knee ligament injury, which will rule him out for the remainder of this season."
The club added: "Our medical team are now managing Ben's recovery and rehabilitation programme, with everyone fully focused on supporting the aim of Ben being ready for the start of our pre-season preparations."
White will now miss Arsenal's final two Premier League matches against Burnley and Crystal Palace, as well as the Champions League final against Paris Saint-Germain on 30 May.
The injury comes at a difficult time for Arsenal, who are chasing a first league title in 22 years while preparing for their first Champions League final in 20 years.
White had also recently forced his way back into the England setup under Thomas Tuchel after more than three years away from international duty. He made his first appearance since 2022 during the March friendlies and scored against Uruguay national football team.
However, the defender now appears set to miss the FIFA World Cup, with Tuchel due to announce his squad on 22 May.
White's absence also adds to Arsenal manager Mikel Arteta's defensive concerns, with Jurrien Timber still sidelined through injury.
The former Brighton defender has made 30 appearances in all competitions this season, despite struggling with fitness issues over the past two campaigns, including knee surgery last season and a hamstring injury earlier in the current campaign.
Liverpool manager Arne Slot has moved to calm the reaction surrounding his decision to substitute 17-year-old Rio Ngumoha during a tense 1-1 draw with Chelsea at Anfield, insisting the change was driven by fitness concerns rather than tactics.
Manchester City manager Pep Guardiola believes Jeremy Doku has the potential to reach the level of top wingers such as Vinicius Junior and Lamine Yamal after the Belgian continued his impressive scoring run in Saturday's 3-0 win over Brentford.
Newcastle head coach Eddie Howe has admitted he is already planning for next season after leaving Anthony Gordon on the bench for a second successive game amid growing interest from Bayern Munich.
Mikel Arteta praised the officials for making a "big call" after VAR ruled out Callum Wilson's late equaliser to secure Arsenal a dramatic 1-0 victory over West Ham United on Sunday.
