Williamson went down in pain 12 minutes into their 1-0 loss to United on Wednesday and she was helped off the pitch by medical staff before limping down the tunnel.
ACL injuries generally require months of recovery and rehabilitation, and her injury is a huge blow for European champions England with the World Cup kicking off in July.
"Leah will now begin a period of rehabilitation and is set for an extended spell on the sidelines. She will undergo surgery in due course," Arsenal said in a statement on Friday.
The injury also damages Arsenal's hopes with the club third in the league standings - six points behind leaders United - while they are also in the Champions League semi-finals with the first leg against VfL Wolfsburg on Sunday.
Arsenal had already lost captain Kim Little for the rest of the season due to a hamstring injury while forward Vivianne Miedema also had her season ended due to an ACL injury in December.
Miedema, the Netherlands' record goalscorer, also said she would miss the World Cup after undergoing surgery.
Arsenal women's boss Jonas Eidevall blamed the conditions of the Leigh Sports Village pitch after Williamson suffered her injury.
"I think if you see the pitch... it is a pitch that has a lot more to ask for and I think it's going to continue here with the playing schedule," he had said after the game.
"Playing on pitches like that, of course players are going to get injured. It's something we all need to improve on, the facilities where we play, if we want to keep the players on the pitch."
Beth Mead also ruptured her ACL in November and England boss Sarina Wiegman said last month that it would take a 'miracle' for the Arsenal striker and Euros top scorer to be ready for the tournament.
