The Argentinian, a January signing from Fiorentina, twisted his knee awkwardly towards the end of the first half of the 1-1 draw against his former club.
Zarate required oxygen and nine minutes of treatment on the pitch before he was carried off on a stretcher and taken to hospital for scans.
And on Sunday the 29-year-old revealed the extent of the damage in an Instagram post.
He wrote: "With sadness I inform you that the results show the following: anterior cruciate ligament rupture plus an injury grade 1 of medial collateral ligament.
"I will face this with all my strength and will be back stronger than before."
Zarate was making just his third appearance for the Hornets and earned the penalty with which Troy Deeney opened the scoring, but he now faces a lengthy spell on the sidelines.
West Ham boss Slaven Bilic has better injury news and is hopeful Andy Carroll will be fit to face Chelsea in their next match a week on Monday.
The striker missed Saturday's 1-1 draw at Watford with a groin problem but Bilic expects him back in full training by Wednesday at the latest.
"The guys from the medical department have told me he's going to start training Tuesday or Wednesday," said the Hammers manager.
"He ran on Friday and Saturday morning with no negative reaction, so hopefully. Me and my medical department are fighting. They say Wednesday, I say Tuesday.
"Then hopefully four or five days of training, that is always enough for Andy to shine in the next game. So hopefully he is going to be able to play against Chelsea."
Carroll, who has scored four goals in his last four matches, was missed as West Ham squandered a host of chances to cancel out Deeney's early penalty at Vicarage Road.
But Andre Ayew, on his first appearance since returning from the African Nations Cup with Ghana, grabbed the equaliser eight minutes after coming on as a 65th minute substitute.
Michail Antonio - who was later sent off for a second yellow card - somehow hit both posts before the ball popped out to Ayew, who tucked in his second goal for the Hammers.
"It was a fair result - they had the first half and we had the second," said Ayew.
"It was a tough game, this is the Premier League. We just need to keep working hard and hopefully we'll get the results we want.
"For the goal the ball came to me off both posts. That's the game and sometimes that's how it comes, sometimes it doesn't, but that's football.
"For me it was important to score in my first game back. I will continue to work hard and hopefully I can get some more goals."
